Given a marginal p.m.f of x (f₁(x)) that distribute (EJ)uniformly on 1 and 2and a marginal p.m.f of y (f₂(y)) that distribute (EJ)uniformly on 10 and 22x and y are stochastically independent r.v.sthen the J.p.m.f of x and y (f(x,y) ) isfor x = 1,2f(x, y) =y = 10,22,O.WOption 2f(x, y) =0f(x, y) =for x = 1,2y = 10,22,O.WOption 1(1 for x = 1,2y = 10,22,O.W0-{²0

Answered: Given a marginal p.m.f of x (f₁(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...

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There are only two states of the world, when a person is well with probability (1-p) and ill with probability p, where (1-p)= 1/3 and p = 2/3. Consider Adam who has utility function U = (Y1, Y2,1 – p,p) = Y,"-P)Y?, where Y; is the income and i =1 is well and i = 2 is ill. When Adam is well, he earns $1000, but when he is ill, he losses $300 in health expenditures and earnings such that Y2 = $700. What is the maximum total premium that Adam is still willing-to-pay? (1-р).
4. Let X and Y have the joint pmf defined by f(0,0) = f(2,1) = 0.3, f(1,0) = f(1,1) = 0.2(a) Depict the points and corresponding probabilities on a graph.(b) Give the marginal pmfs in the “margins.”(c) Compute μX, μY, σ2X, σ2Y, Covariance(X,Y ), and ρ.(d) Find the equation of the least squares regression line and draw it on your graph. Doesthe line make sense to you intuitively?
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5. (Sec. 5.1) Suppose the marginal pdfs of two independent rvs X and Y are given by 5x4 for 0 |0 otherwise 1 fx(r) 2y3for 0y <1 |0 otherwise fy(y) (a) Find the joint pdf of X and Y (b) What is the probability that both X and Y are greater than .5? (c) What is the probability that at least one of X or Y is greater than .5?
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Suppose that Y₁ and Y₂ are uniformly distributed over the triangle shaded in the accompanying figure. 3₂ (0, 1) (-1,0) (a) Find Cov(Y₁ Y₂). Cov(Y₁, Y₂) = (b) Are Y₁ and Y₂ independent? Yes O No (1, 0) (c) Find the coefficient of correlation for Y₁ and Y₂. P= y/₁ (d) Does your answer to part (b) lead you to doubt your answer to part (a)? Why or why not? O Even though Cov(Y₁Y₂) # 0, Y₁ and Y₂ are not necessarily dependent. Since Cov(Y₁ Y₂) # 0, we should expect Y₁ and Y₂ to be dependent. O Since Cov(Y₁, Y₂) = 0, we should expect Y₁ and Y₂ to be independent. O Even though Cov(Y₁Y₂) = 0, Y₁ and Y₂ are not necessarily independent.
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2) If the random variable (x) uniformly distributed on the interval (-2,4), then the moment generating function Mx(t) = e4t а) -e-2t e4t. b) -e-2t -6t 6t e 4t -e2t e4t d) +e-2t 6t 6t

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