In this problem there are two random variables X and Y. The random variable Y counts...

In this problem there are two random variables X and Y. The random variable Y counts how many times we roll the die in the following experiment: First, we flip a fair coin. If it comes Heads we set X= 1 and roll a fair die until we get a six. If it comes Tails, we set X= 0 and roll the die until we get an even number (2, 4 or 6).

a). What are the possible values taken by the pair (X,Y)? What is the probability that (X,Y) =(0,k) fork= 1,2,...? What is the join mass distribution function of the pair (X,Y)?

b). What is the mass distribution of the second marginal of (X,Y), that is, the mass distribution of Y?

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Given two random variables x and y State of Nature Probability variable x variable y I...

Given two random variables x and y State of Nature Probability variable x variable y I 0.2 18 0 II 0. 2 5 -3 III 0.2 12 15 IV 0.2 4 12 V 0.2 6 1 (i) Calculate the mean and variance of each of these variables and the covariance between them (ii) Suppose x and y represent the returns from two assets. Calculate the mean and variance for the following part folios. % in x 125 100 75 50...

Consider the two dependent discrete random variables X and Y . The variable X takes values...

Consider the two dependent discrete random variables X and Y . The variable X takes values in {−1, 1} while Y takes values in {1, 2, 3}. We observe that P(Y =1|X=−1)=1/6 P(Y =2|X=−1)=1/2 P(Y =1|X=1)=1/2 P(Y =2|X=1)=1/4 P(X = 1) = 2/ 5 (a) Find the marginal probability mass function (pmf) of Y . (b) Sketch the cumulative distribution function (cdf) of Y . (c) Compute the expected value E(Y ) of Y . (d) Compute the conditional expectation...

Let X and Y be two independent random variables such that X + Y has the...

Let X and Y be two independent random variables such that X + Y has the same density as X. What is Y?

Problem 2. (a) Prove that, if two continuous random variable X and Y are independent P(X...

Problem 2. (a) Prove that, if two continuous random variable X and Y are independent P(X > x, Y > y) = P(X > x)P(Y > y) (b) Now prove that, under the same conditions, X,Y, independent continuous random variables, E(XY) = E(X)E(Y).

Provide an example that if the cov(X,Y) = 0, the two random variables, X and Y,...

Provide an example that if the cov(X,Y) = 0, the two random variables, X and Y, are not necessarily independent. Would you please give the example specifically and why?

Provide an example that if the cov(X,Y) = 0, the two random variables, X and Y,...

Provide an example that if the cov(X,Y) = 0, the two random variables, X and Y, are not necessarily independent. Would you please give the example specifically and why?

Let X and Y be two independent random variables. X is a binomial (25,0.4) and Y...

Let X and Y be two independent random variables. X is a binomial (25,0.4) and Y is a uniform (0,6). Let W=2X-Y and Z= 2X+Y. a) Find the expected value of X, the expected value of Y, the variance of X and the variance of Y. b) Find the expected value of W. c) Find the variance of W. d) Find the covariance of Z and W. d) Find the covariance of Z and W.

This is the probability distribution between two random variables X and Y: Y \ X 0...

This is the probability distribution between two random variables X and Y: Y \ X 0 1 2 3 0.1 0.2 0.2 4 0.2 0.2 0.1 a) Are those variables independent? b) What is the marginal probability of X? c) Find E[XY]

A random sample of two variables, x and y, produced the following observations: x y 19...

A random sample of two variables, x and y, produced the following observations: x y 19 7 13 9 17 8 9 11 12 9 25 6 20 7 17 8 Compute the correlation coefficient for these sample data. Group of answer choices a. -0.9707 b. -0.2141 c. 0.5133 d. 0.8612

Question 1: Two jointly distributed discrete random variables Consider two discrete random variables X, Y ,...

Question 1: Two jointly distributed discrete random variables Consider two discrete random variables X, Y , taking values in {0, 1, 2, 3} each (for a total of 16 possible points). Their joint probability mass function is given by fXY (x, y) = c · x+1 y+1 . Answer the following questions. (a) What is c? (b) What is the probability that X = Y ? (c) Derive the marginal probability mass functions for both X and Y . (d)...

Subjects