Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following.x < 0x2F(x) =OSx< 5255 S xUse the cdf to obtain the following. (If necessary, round your answer to four decimal places.)(a) Calculate P(X S 3).0.36(b) Calculate P(2.5 SXS 3).0.11(c) Calculate P(X > 3.5).0.51(d) What is the median checkout duration u? [solve 0.5 = F(M)].Enter a number.(e) Obtain the density function f(x).f(x) = F'(x)OSx < 5otherwise(f) Calculate E(X).(g) Calculate V(X) and oV(X)(h) If the borrower is charged an amount h(X) = x² when checkout duration is X, compute the expected charge E[h(X)].

I solved exactly three subparts because of bartleby policy if you want more please upload…

Answered: (d) What is the median checkout…

(d) What is the median checkout duration i? [solve 0.5 = F(M)). Enter a number. (e) Obtain the density function f(x). F(x) = F'(x) Osx < 5 otherwise (f) Calculate E(X).

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: The pdf of a continuous RV X is given by: f(x)=12xf(x)=12x ,„XE[1,e2]x=[1,e2]. 1. find P(x>10) 2.…

A: Given Data : Probability Density function of continuous random variable X is given by :…

Q: Let x denote the amount of gravel sold (in tons) during a randomly selected week at a particular…

Q: Find i) Partial derivative. tii) of the function i Z= 200+xy Level Sur face エエ

A: Given z=200+x2y2 i) Partial derivative zx=0+2xy2=2xy2zy=0+2x2y=2x2y ii) Level surface of the…

Q: Let h(x) = V4+ 3f(x) with f(1) = 7 and f'(1) = 4. Find the value of h'(1).

Q: Use the total differential to find the slopes of the indiffa of the following utility functions: a)…

A: a) slopes of the indifference of the following utility functions ux1,x2=x1x2 mux1=dux1,x2dx1=x2…

Q: Find the values of the random variable Z and complete the table.

A: Here 4 coins are tossed

Q: Let y Δy ~ = 3x² + 5x +4. If Ax = 0.1 at x = 5, use linear approximation to estimate Ay

Q: Find df / dx and ðf / dy. f(x,y) = e(x + y + 8)

Q: Find the revenue function R(x) when the marginal revenue is R'(x) = 400 - 0.4x and no revenue…

A: Given marginal revenue function R'( x ) = 400 - 0.4x

Q: 4,5 f (x,V)= Sx"y%,compute fx and fy

Q: Find the equation of normal to the function f(x)=x3−3x+1 at its local maximum point. I want a HUMAn…

A: The objective of this question is to find the equation of the normal line to the function f(x) = x^3…

Q: Let x denote the amount of gravel sold (in tons) during a randomly selected week at a particular…

A: For the given f(x ) Find (a) P (x> 1/4 ) = ? ( b ) P( X>=1/8 ) =>

Q: 13) The market research department for an automobile company estimates that sales (in millions of…

A: Given data: The expression for the rate at which electric car increases is S'(t)=4e-0.08t. The given…

Q: Let X ~ exp(rate = 3). (a) Find the mgf of X. (b) Use the mgf to find E[X], Var(X), E[X4] and E[X").

Q: During a Formula 1 test. 25% of the cars that participated in the test experienced a tire blowout.…

A: Correct answer is (C) 0.1484

Q: (b) For a differentiable function f(x), show that 8(2 = 1) where f' = dj ]dx and a; are the values…

A: We will use the following properties of Dirac delta function to prove the given formula : ∫abδxdx=1…

Q: Describe an assumption that we are making about the distribution of the beans after “frolicking,”…

A: When marked beans are added back to the population in the cup, the researcher ask to 'frolic' or mix…

Q: Let f(x) = e*g(x), where g(0) = 1 and g'(0) = 4. Find f'(0). %3D %3D

A: fx=exgx Differentiating with respect to x, we get f'x=dexdx·gx+dgxdx·ex…

Q: Let h(x) = If f(2) = 1 and f'(2) = -1, find h'(2). A B C OD E A. 36 B. 27 C. 12 D. -12 E. 48

A: Step 1:To solve the problem, let's break it down step by step.Given the function:h(x)=[f(x)x]3We…

Q: Let Fbe a function of two variables, defined by F(K, L) = 9 In K+ 4 In L. %3D (a) Find RK = F,'(K,…

A: We have to find marginal rate and elasticity of the substitution.

Q: fxx (x, y) = (x + y²), 0sx<1,0<ys1 a) What is the marginal pdf of fy (y)? b) What is the conditional…

A: Solution: From the given information,

Q: ) L(3.98) where L(x) is the linearization of y = √√x +3 at x = 1 (tangent line approximation)

Q: Why is F(x) considered an accumulation function?

A: An accumulation function is a function that gives the “area” under the thegraph of a function y =…

Q: (4) The mass (in grams) of an insect after t days is given by m(t) = 3+t2, while the volume (in cm³)…

Q: The linear approximation L(x) of a differentiable function f(x) near the point x = a is L(x) = f'(a)…

A: Given statement is false, because

Q: Which of the following expressions best match the given statement provided that f(t) = F'(t). The…

A: Given thatf(t)=F'(t)

Question

Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following.
x < 0
x2
F(x) =
OSx< 5
25
5 S x
Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)
(a) Calculate P(X S 3).
0.36
(b) Calculate P(2.5 SXS 3).
0.11
(c) Calculate P(X > 3.5).
0.51
(d) What is the median checkout duration u? [solve 0.5 = F(M)].
Enter a number.
(e) Obtain the density function f(x).
f(x) = F'(x)
OSx < 5
otherwise
(f) Calculate E(X).
(g) Calculate V(X) and o
V(X)
(h) If the borrower is charged an amount h(X) = x² when checkout duration is X, compute the expected charge E[h(X)].

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here