statistics

Statistical Inference I: J. Lee Assignment 5

Problem 1. Two fair dice are rolled. Find the joint probability mass function of X and Y , where X is the largest value obtained on any die, and Y is the sum of the values on the two dice.

Problem 2. Suppose that X and Y have joint mass function as shown in the table below. (Here, X takes on possible values in the set {−2, 1, 3}, Y takes on values in the set {−2, 0, 1, 3.1}.)

-2 0 1 3.1 -2 .1 .2 0 0 1 .1 0 .4 0 3 0 .1 0 .1

(a) Compute P(X2 > Y ).

(b) Find the marginal mass function of X and plot it. (be very explicit!)

(c) Compute var(X2).

Problem 3. Suppose that X and Y have the joint pmf (probability mass function), with:

p(−2,−1) = .1, p(−2, 0) = .1, p(−2, 2) = .1, p(0, 2) = .1, p(1,−1) = .2, p(1, 0) = .1, p(1, 2) = .2, p(1, 3) = .1.

(a) Find the marginal probability mass function of Y . (be explicit!)

(b) Compute the covariance of X and Y , which is given by cov(X, Y ) = E(XY )−E(X)E(Y ).

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