Question

Let X denote the amount of time a book on two-hour reserve is actually checked out,...

Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following.

F(x) =
0      x < 0
x2
16
0 ≤ x < 4
1 4 ≤ x

Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)

(a) Calculate P(X ≤ 2).


(b) Calculate P(1.5 ≤ X ≤ 2).


(c) Calculate P(X > 2.5).


(d) What is the median checkout duration ? [solve 0.5 = F()].


(e) Obtain the density function f(x).
f(x) = F '(x) =



(f) Calculate E(X).


(g) Calculate V(X) and σx.

V(X) =
σx =


(h) If the borrower is charged an amount h(X) = X2 when checkout duration is X, compute the expected charge

E[h(X)].

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let X denote the amount of time a book on two-hour reserve is actually checked out,...
Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is F(x) = 0           x < 0 F(x) = x2/4       0 ≤ x < 2 F(x) = 1           2 ≤ x Use the cdf to obtain the following a) P[ X ≤ 1 ] b) P[ 0.5 ≤ X ≤ 1 ] c) P[ X > 1.5 ] d) Expected value of X, E[X] e) Variance of X, Var[X]
Let X denote the amount of time for which a statistics reference book, on two-hour reserve...
Let X denote the amount of time for which a statistics reference book, on two-hour reserve at the library, is checked out by a randomly selected student. Suppose that X has the following probability density function (pdf) f(x)=kx2(2−x), 0≤x≤2. (a) Find the cumulative distribution function (cdf) of X (Hint: Don’t forget that first you have to find k). (b) Find the probability that the book is checked out for a time between 0.5 and 1.5 hours. (c) Find the probability...
Part 1 The Rockwell hardness of a metal is determined by impressing a hardened point into...
Part 1 The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point. Suppose the Rockwell hardness of a particular alloy is normally distributed with mean 72 and standard deviation 3. (b) If the acceptable range of hardness is (72 − c, 72 + c), for what value of c would 95% of all specimens have acceptable hardness? (Round your answer to...
Let X denote the amount of space occupied by an article placed in a 1-ft3 packing...
Let X denote the amount of space occupied by an article placed in a 1-ft3 packing container. The pdf of X is below. f(x) = 90x8(1 − x)      0 < x < 1 0 otherwise (a) Graph the pdf. Obtain the cdf of X. F(x) =      0 x < 0 x9(10−9x)    0 ≤ x ≤ 1      1 x > 1 Graph the cdf of X. (b) What is P(X ≤ 0.65) [i.e., F(0.65)]? (Round your answer to four...
Given a random variable X has the following pmf: X -1 0 1 P[X] 0.25 0.5...
Given a random variable X has the following pmf: X -1 0 1 P[X] 0.25 0.5 0.25 Define Y = X2 & W= Y+2. Which one of the following statements is not true? A) V[Y] = 0.25. B) E[XY] = 0. C) E[X3] = 0. D) E[X+2] = 2. E) E[Y+2] = 2.5. F) E[W+2] = 4.5. G) V[X+2] = 0.5. H) V[W+2] = 0.25. I) P[W=1] = 0.5 J) X and W are not independent.
Given a random variable X has the following pmf: X -1 0 1 P[X] 0.25 0.5...
Given a random variable X has the following pmf: X -1 0 1 P[X] 0.25 0.5 0.25 Define Y = X2 & W= Y+2. Which one of the following statements is not true? A) V[Y] = 0.25. B) E[XY] = 0. C) E[X3] = 0. D) E[X+2] = 2. E) E[Y+2] = 2.5. F) E[W+2] = 4.5. G) V[X+2] = 0.5. H) V[W+2] = 0.25. I) P[W=1] = 0.5 J) X and W are not independent.
Let X1, X2 be two normal random variables each with population mean µ and population variance...
Let X1, X2 be two normal random variables each with population mean µ and population variance σ2. Let σ12 denote the covariance between X1 and X2 and let ¯ X denote the sample mean of X1 and X2. (a) List the condition that needs to be satisfied in order for ¯ X to be an unbiased estimate of µ. (b) [3] As carefully as you can, without skipping steps, show that both X1 and ¯ X are unbiased estimators of...
The weekly demand for propane gas (in 1000s of gallons) from a particular facility is an...
The weekly demand for propane gas (in 1000s of gallons) from a particular facility is an rv X with the following pdf. f(x) = 2 1 − 1 x2      1 ≤ x ≤ 2 0 otherwise (a) Compute the cdf of X. F(x) =     0 x < 1 1 ≤ x ≤ 2     1 2 > x (b) Obtain an expression for the (100p)th percentile. η(p) = What is the value of ? (Round your answer to three decimal...
The weekly demand for propane gas (in 1000s of gallons) from a particular facility is an...
The weekly demand for propane gas (in 1000s of gallons) from a particular facility is an rv X with the following pdf. f(x) = 2 1 − 1 x2      1 ≤ x ≤ 2 0 otherwise (a) Compute the cdf of X. F(x) =     0 x < 1 1 ≤ x ≤ 2     1 2 > x (b) Obtain an expression for the (100p)th percentile. η(p) = What is the value of ? (Round your answer to three decimal...
A mail-order computer software business has six telephone lines. Let x denote the number of lines...
A mail-order computer software business has six telephone lines. Let x denote the number of lines in use at a specified time. The probability distribution of x is as follows: X P(x) 0 0.11 1 0.17 2 0.20 3 0.25 4 0.15 5 0.08 6 0.04 Calculate the probability of: (a). at most three lines are in use. (b). fewer than three lines are in use. (c). at least three lines are in use. (d). between two and five lines...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT