.1. A random variable X has pdf fx(x) = 22\e^-x, x > 0. (a) Use Chebyshev's inequality to obtain an upper bound for P(X € (ux – 1,ux + 1)) (b) Use Chebyshev's inequality to obtain a lower bound for P(X € (ux - 3, ux + 3))
Answers
The lower bound for P(X ∈ (uX - 3, uX + 3)) is given by P(|X - u| > 2σ) ≤ 1/4, These bounds obtained using Chebyshev's inequality provide an estimate of the probability ,
that X falls within the specified intervals (uX – 1, uX + 1) and (uX - 3, uX + 3), respectively. (a) Chebyshev's inequality states that for any random variable X with mean μ and standard deviation σ,
the probability that X deviates from its mean by more than k standard deviations is at most 1/k^2. In this case, the random variable X has a mean μ = u and a standard deviation σ = sqrt(22).
To obtain an upper bound for P(X ∈ (uX – 1, uX + 1)), we need to determine the value of k such that the probability of X deviating from its mean by more than k standard deviations is at most 1/2.
Using Chebyshev's inequality, we have: P(|X - u| > kσ) ≤ 1/k^2
Setting the right-hand side to 1/2, we can solve for k:
1/k^2 = 1/2
k^2 = 2
k = sqrt(2)
Therefore, the upper bound for P(X ∈ (uX – 1, uX + 1)) is given by:
P(|X - u| > sqrt(2)σ) ≤ 1/2
(b) To obtain a lower bound for P(X ∈ (uX - 3, uX + 3)), we need to determine the value of k such that the probability of X deviating from its mean by more than k standard deviations is at most 1/4.
Using Chebyshev's inequality, we have: P(|X - u| > kσ) ≤ 1/k^2
Setting the right-hand side to 1/4, we can solve for k:
1/k^2 = 1/4
k^2 = 4
k = 2
Therefore, the lower bound for P(X ∈ (uX - 3, uX + 3)) is given by:
P(|X - u| > 2σ) ≤ 1/4
These bounds obtained using Chebyshev's inequality provide an estimate of the probability that X falls within the specified intervals (uX – 1, uX + 1) and (uX - 3, uX + 3), respectively.
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Related Questions
E1.8 (lo 2), ap evilene company makes industrial-grade brooms. it incurs the following costs.
1. salaries for broom inspectors.
2. copy machine maintenance at corporate headquarters.
3. hourly wages for assembly workers.
4. research and development for new broom types.
5. salary for factory manager.
6. depreciation on broom-assembly equipment.
7. salary for the ceo administrative assistant.
8. wood for handles.
9. factory cleaning supplies.
10. lubricants for broom-assembly factory equipment.
11. salaries for customer service representatives.
12. salaries for factory maintenance crew.
13. sales team golf outings with customers.
14. salaries for the raw materials receiving department employees. 1
5. advertising expenses. 1
6. depreciation on the cfo company car.
17. straw for brooms. 1
8. salaries for sales personnel.
19. shipping costs to customers.
instructions a. indicate whether each cost is direct materials, direct labor, manufacturing overhead, or nonmanufacturing.
indicate whether each cost is a product cost or a period cost.
Answers
Based on the costs to AP Evilene Company which makes industrial-grade brooms, the classifications of the costs are:
Product and ManufacturingPeriod and nonmanufacturing Product and Direct labor Period and nonmanufacturing Product and ManufacturingProduct and ManufacturingPeriod and nonmanufacturing Product and Direct materialsProduct and ManufacturingProduct and ManufacturingPeriod and nonmanufacturingProduct and ManufacturingPeriod and nonmanufacturing Period and nonmanufacturing Period and nonmanufacturing Period and nonmanufacturing Product and Direct materialsPeriod and nonmanufacturing Period and nonmanufacturing What are the types of costs?There are period costs which are those which are only incurred in a period of production and are not related to production of goods and services but instead to the selling of them.
Product costs are incurred when the business produces a good or service. They can be direct labor or materials, or a manufacturing overhead that is indirectly related to production.
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At a college, 70 percent of the students are women and percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Use this contingency table C Women 45 25.70 Men .05 .25 .30 .50 .50 1.00 What is the probability that a student is female and a C student ? A. .45 B..50 C. .70 D. 25 E..05
Answers
The probability that a student is female and a C student is 0.5.
We need to find the probability that a student is female and a C student, given that 70% of students are women, 30% of students receive a grade of C, and 25% of students are neither female nor C students. We can use the contingency table given as follows:
Since 70% of students are women, we can find the probability of selecting a female student by adding the probability of selecting a female student who received either an A, B, or C grade. Thus, the probability of selecting a female student is:
P(Female) = P(Female, A) + P(Female, B) + P(Female, C) = 0.05 + 0.25 + 0.45 = 0.75
Similarly, the probability of selecting a C student is:P(C) = P(A, C) + P(B, C) + P(Female, C) + P(Male, C) = 0.05 + 0.1 + 0.45 + 0.3 = 0.9
Now, let's find the probability of selecting a student who is neither female nor C student: P(Neither female nor C) = 0.25From the given contingency table, we have:P(Female, C) = 0.45Thus, we can use the formula for conditional probability to find the probability of selecting a female student who is also a C student: P(Female | C) = P(Female, C) / P(C) = 0.45 / 0.9 = 0.5
In a college, 70 per cent of the students are women and per cent of the students receive a grade of C. 25 per cent of the students are neither female nor C students. In order to find the probability that a student is female and a C student, given that 70% of students are women, 30% of students receive a grade of C, and 25% of students are neither female nor C students, we used the given contingency table. Using this contingency table, we calculated the probabilities of selecting a female student and a C student separately. We also calculated the probability of selecting a student who is neither female nor C student. Finally, we used the formula for conditional probability to find the probability of selecting a female student who is also a C student. The probability that a student is female and a C student is 0.5. Therefore, option (B) is the correct answer
The probability that a student is female and a C student is 0.5.
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An antique store increases all of its prices by 40$ and then announces a 25 off-everything sale. What percent of the original prices (before the increase) is the new prices?
Answers
Answer: 62.5%.
hope this helped
Find the slope, or rate of change, from the graph.
answer please correct answers
Answers
Answer:
3/2
Step-by-step explanation:
slope is rise over run
or y change divided by x change
to find the slope you need to find points on the graph that meet exact points on the graph
i see (0,0) and (4,6)
to find slope without graph it would be (y2-y1)/(x2-x1)
in this case (6-0)/(4-0)
=6/4
=3/2
=1 1/2
with graph you can count that it goes up 3 squares while moving two squares to the right
3/2
hope this helps
HELP ASAP I will mark brainliest
Answers
Answer:
option 4
Step-by-step explanation:
Design DFA {w ∈ Σ ∗ | number of 0’s in w is a multiple of 3 and number of 1’s in w is odd }.
Answers
The resulting DFA will have four states (A, B, C, D) and transitions defined as described above. State D will be the only final state.
To design a DFA that accepts strings where the number of 0's is a multiple of 3 and the number of 1's is odd, we can follow these steps:
1. Define the DFA states:
- We need to keep track of two things: the count of 0's (mod 3) and whether the count of 1's is odd or even.
- Let's define four states: A, B, C, and D.
- State A represents the initial state with a count of 0's = 0 and an even count of 1's.
- State B represents a count of 0's = 1 (mod 3) and an even count of 1's.
- State C represents a count of 0's = 2 (mod 3) and an even count of 1's.
- State D represents any count of 0's (mod 3) and an odd count of 1's.
2. Define the transitions:
- From state A, if we read a 0, we transition to state B (count of 0's = 1 (mod 3)).
- From state A, if we read a 1, we transition to state D (odd count of 1's).
- From state B, if we read a 0, we transition to state C (count of 0's = 2 (mod 3)).
- From state B, if we read a 1, we transition to state D (odd count of 1's).
- From state C, if we read a 0, we transition to state A (count of 0's = 0 (mod 3)).
- From state C, if we read a 1, we transition to state D (odd count of 1's).
- From state D, if we read either a 0 or a 1, we stay in state D.
3. Define the final (accepting) state:
- State D is the final state since it represents the condition of having a count of 0's (mod 3) and an odd count of 1's.
The resulting DFA will have four states (A, B, C, D) and transitions defined as described above. State D will be the only final state.
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Complete question is below
Design DFA {w | w ∈ Σ ∗ | number of 0’s in w is a multiple of 3 and number of 1’s in w is odd }.
plz help
On Monday, Elsbeth’s bank account balance was -$16.75. On Tuesday, she deposited a check for $5.72. On Thursday, she deposited $16.75. What is her new balance?
-16.75 + (5.72 + 16.75)
Use the commutative property to get:
-16.75 + (16.75 + 5.72)
Use the associative property to get:
(-16.75 + 16.75) + 5.72
On Friday, Elsbeth deposited her pay check for $872.56. What was the account’s final total?
-$866.84
$878.28
$895.03
$903.10
Answers
Answer:
$5.72
Step-by-step explanation:
Sorry I was late--
The distance between two hotels on a map is 3.4 centimeters (cm). The map uses a scale of 1 cm = 100 kilometers (km). How far apart are the hotels?
Answers
Answer:
1020km
Step-by-step explanation:
1cm=300km
3.4cm= 1020km
please mark as brainliest!!!<3<3
What is 5(pi) /6 radians converted to degrees? If necessary, round your answer to the nearest degree
ANSWER IS 150 DEGREES
Answers
Answer:
C
Step-by-step explanation:
By converting radians 5π /6 into a degree, we get the nearest degree 150.
How to convert radians into a degree?
We can convert radians into a degree by using the formula
Degree = Radians x (180°) / π
To 5π /6 convert radians into a degree,
Degree = Radians x (180°) / π
Degree = 5π /6 x (180°) / π
= 5 /6 x (180°)
= 150°
Learn more about Degree;
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please help me thank you
Answers
Answer:
7<x<14
Step-by-step explanation:
Answer:
heh heh that's a hard one
(6−3x
2
−8x
4
−2x
3
)+(6+7x
2
)+(2−7x
3
+3x
2
)
What is the constant?
Answers
Answer:
14
Step-by-step explanation:
I tried to put the problem together as best as I could and i got the problem as (6-3x^2-8x^4-2x^3)+(6+7x^2)+(2-7x^3+3x^2)
That means that the constants are 6+6+2.
6+6+2= 14
Write the quadratic equation whose roots are -3 and -1, and whose leading coefficient is 3.
(Use the letter x to represent the variable.)
Answers
The quadratic equation will be; 3x² + 6x + 9
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Given that roots are x = -3 and x = - 1, and whose leading coefficient is 3.
The factors are; (x + 3) and (x + 1)
f(x) = a(x + 3)(x + 1)
As, a = 3.
Then we get;
f(x) = 3(x + 3)(x + 1)
= 3(x² + 2x + 3)
= 3x² + 6x + 9
The quadratic equation will be; 3x² + 6x + 9
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What’s v=1/3 pi r to the power of 2 h?
Answers
The cone has a height of h = \(\frac{3V}{\pi r^{2} }\)
What is the cone's volume?A geometric object with a three-dimensional shape is called a cone. It features two distinct surfaces, referred to as flat and curved surfaces. A cone is created by connecting the two surfaces. One-third of the area of the base B times the height h equals the volume V of a cone with radius r. The volume of an oblique cone may be calculated using the same formula as a right cone. The volumes of a pyramid and a prism are connected, just as the volumes of a cone and a cylinder are related.
The answer to the question is the provided expression, which represents the cone's volume;
It is spelled as follows:
Volume (V) = \(\frac{1}{3}\pi r^{2}h\)
Now, the formula for calculating height 'h' is displayed below:
h = \(\frac{3V}{\pi r^{2} }\)
As a result, h = \(\frac{3V}{\pi r^{2} }\) is the cone's height.
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Write the equation of the line parallel to x+7y=21 that passes through the point (–14, 4).
Answers
Answer:
Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.
First, rearrange x + 7y = 21 into y = mx + c form.
x + 7y = 21
7y = - x + 21
y = -1/7x + 3
Parallel lines have the same gradient so gradient of line is -1/7.
Equation of line is now y = -1/7x + c.
Substitute (-14,4) into the equation to find c.
4 = -1/7(-14) + c
4 = 2 + c
c = 2
Hence, equation of line is y = -1/7x + 2.
What is 9.14 divided by 0.04
Answers
[Mathematical Problem]
\(9.14\) ÷ \(0.04\)
Solution:
\(228.5\)
Hope this helps! Thanks and good luck!
If you’re willing to help, that’d be nice.
Answers
Answer:
tw ni oe haso layo esma question sodnww aokos
Up to this point, the only types of numbers you've seen have been rational numbers. You can write any rational number as a fraction. The prefix ir- means not. What do you think it means for a number to be irrational? Can you think of any numbers that are irrational?
Answers
Answer:
Since rational numbers can be written as a ratio, such as a/b, then irrational numbers can not be written that way.
Step-by-step explanation:
Square roots of non-perfect squares are irrational numbers because they are non-terminating and non repeating decimals
Which statement about a dilation with a scale factor of 3 is true?
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Given : dilation with a scale factor of 3
To find : Which statement is true
Solution:
A dilation is a transformation that produces an image that is the same shape as the original, but is a different size
if Dilation factor N then image Size is multiplied by N
if Scale factor < 1 then image get reduced
if scale factor > 1 then image get enlarged
scale factor = 1 lead to Same size image
Here is given that Scale factor of 3
=> image will be enlarged to 3 times the original image
Hence correct option is :
C)Each side in the pre-image is multiplied by three to find the corresponding side length in the image
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the scale of drawing of floor plane is 1:200 what is the actual length ...
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why is paying back along with a nominal interest rate of 13.62% if the interest is compounded quarterly, how much greater is white effective interest rate than his nominal interest rate
Answers
The required white effective interest rate is 0.71% more than his nominal interest rate.
What is compound interest?Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.
Here,
White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent
So
Difference in interest = 14.33%-13.62%
=0.71%
Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.
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1. Find the measure of y.
110°
z
yº
100°
87°
Answers
Answer:
97.8263768112
Step-by-step explanation:
Geometric Mean is denoted as 'x'
x = √(110×87)
x = √9570
∴ x = 97.8263768112
Define Geometric MeanThe Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers. In essence, we multiply the numbers together and calculate their nth root, where n is the total number of data values. For instance, the geometric mean for a given pair of numbers, say 3 and 1, is equivalent to (3 + 1) = 3 = 1.732.In other terms, the geometric mean is the product of n numbers divided by the nth root. The geometric mean differs from the arithmetic mean, as is noted. As a result of the fact that in arithmetic mean, the data values are added before being divided by the total number of values. However, when calculating the geometric mean, we multiply the provided data values before taking the root of the entire number of data values using the radical index. Take the square root, for instance, if there are two data points, the cube root if there are three, the fourth root if there are four, and so on.To learn more about Geometric Mean refer https://brainly.com/question/28347817
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PLEASE NO LINKS AND NO NEGATIVITY
Answers
Answer:
B. Combine like terms
Step-by-step explanation:
Inside the parenthesis, they combined -2 and 6 to get a total of 4x
I need help on this it's due in 10 minutes
Answers
Answer:
B, no, yes, no, no, no, 225
Step-by-step explanation:
45 Points- Geometry
HELP ME
Answers
S<--->T
T<--->S
Same thing
4Both sides a equivalent therefore both triangle areas are also equivalent
9514 1404 393
Explanation:
The missing reasons are ...
3. Reflexive property of congruence. A segment is congruent to itself.
4. SSS postulate. The three corresponding sides are shown congruent, so the triangles are congruent.
2x - 2/2x - 3x + 2/4x
Answers
Answer: Solution
−
2
+
2
−
2
x
+
x
2
−2x+2x
Step-by-step explanation: Divide the numbers
2
−
1
⋅
2
2
⋅
−
3
+
2
4
⋅
2
x
Multiply the numbers
2
−
1
⋅
1
−
3
+
2
4
⋅
2
x
−
1
⋅
1
x
−
3
x
+
2
4
⋅
x
2x−1⋅1x−3x+42⋅x
2
−
−
3
+
2
4
⋅
−
1
⋅
2
2
⋅
x
−
3
x
+
2
4
⋅
x
2x−1⋅22⋅x−3x+42⋅x
2
−
1
⋅
1
−
3
+
2
4
⋅
2
x
−
1
⋅
1
x
−
3
x
+
2
4
⋅
x
2x−1⋅1x−3x+42⋅x
Divide the numbers
2
−
−
3
+
2
4
⋅
2
x
−
x
−
3
x
+
2
4
⋅
x
2x−x−3x+42⋅x
2
−
−
3
+
1
2
2
x
−
x
−
3
x
+
1
2
x
2x−x−3x+21x
x/2>-2 solve the inequality
Answers
Hope this helped
A beach ball has a diameter of 10 inches. What is the volume of air contained inside the beach ball? Use 3.14 for pi. Round your answer to the nearest hundredth.
Answers
Answer:
31.4
Step-by-step explanation:
Answer:
523.33 cubic inches
Step-by-step explanation:
Please help!! 50 points and Brainlist if your right!
Answers
Answer: that is correct
Step-by-step explanation:
Answer:
x = 80°
Step-by-step explanation:
x + 50 + 50 = 180
x + 100 = 180
x = 180 - 100
x = 80°
Hope this helps!
Which of the following is a secant on the circle below
Answers
Answer:
RT is more appropriate, though even SU could be called a secant.
Step-by-step explanation:
What is the best first step to solve the inequality 5x - 3 2 2?
Answers
Answer:
get like terms and make all numbers on one side and variables on the other
Step-by-step explanation:
The third and fourth number in an exponential sequence 100 and 500. what are the first and second numbers in this sequence?
Answers
Answer:
4 and 20
Step-by-step explanation:
100 times 5 is 500. If we go backwards 500 ÷ 5 = 100.
100 ÷ 5 = 20. 20 ÷ 5 = 4.
An exponential sequence is a sequence that grows more every time. It would get really big really quickly.
The first and second numbers in this sequence is 4 and 20
Given that,
The third and fourth number in an exponential sequence 100 and 500.Based on the above information, the calculation is as follows:
\(= 500 \div 100\)
= 5
And,
\(= 100 \div 5 = 20, \\\\20 \div 5 = 4\)
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