please give a thumbs up if you like the solution
20. (8 points) Suppose X, Y, and Z are discrete random variables with joint probability mass...
1. Suppose X and Y are discrete random variables with joint probability mass function fxy defined by the following table: 3 y fxy(x, y) 01 3/20 02 10 7/80 3/80 1/5 1/16 3/20 3/16 1/8 2 3 2 3 a Find the marginal probability mass function for X. b Find the marginal probability mass function for Y. c Find E(X), EY],V (X), and V (Y). d Find the covariance between X and Y. e Find the correlation between X and...
3. Suppose X, Y are discrete random variables taking values in -1,0,1) and their joint probability mass function is 0 0 0 where a, b are two positive real numbers. (i) Find the values of a and b such that X and Y are uncorrelated (ii) Show that X and Y cannot be independent
3. Suppose X, Y are discrete random variables taking values in {-1,0,1) and their joint probability mass function is 0 X=1 where a, b are two positive real numbers. (i) Find the values of a and b such that X and Y are uncorrelated. (ii) Show that X and Y cannot be independent 0
Problem 5 Define X and Y to be two discrete random variables whose joint probability mass function is given as follows: e-127m5n-m P(X = m, Y = n) = m!(n - m)! for m <n, m> 0 and n > 0, while P(X = m, Y = n) = 0 for other values of m, n 1. Calculate the probability that 1 < X <3 and 0 <Y < 2. 2. Calculate the marginal probability mass functions for the random...
If the joint probability distribution of three discrete random variables X, Y , and Z is given by: f(x, y, z) = (x + y)z / 63 , for x = 1, 2; y = 1, 2, 3; z = 1, 2. Find the probability P(X = 2, Y + Z ≤ 3)
Question 4: Let X and Y be two discrete random variables with the following joint probability distribution (mass) function Pxy(x, y): a) Complete the following probability table: Y 2 f(x)=P(X=x) 1 3 4 0 0 0.08 0.06 0.05 0.02 0.07 0.08 0.06 0.12 0.05 0.03 0.06 0.05 0.04 0.03 0.01 0.02 0.03 0.04 2 3 foy)=P(Y=y) 0.03 b) What is P(X s 2 and YS 3)? c) Find the marginal probability distribution (mass) function of X; [f(x)]. d) Find the...
pleaze help me fast 2. Let X and Y be discrete random variables with joint probability mass function X=1 X=5 Y=1 5a За Y=5 4a 8а a. What is the value of a? b. What is the joint probability distribution function (PDF) of X and Y? c. What is the marginal probability mass function of X? d. What is the expectation of X? e. What is the conditional probability mass function of X given Y = 1? f. Are X...
The joint probability density function of the random variables X, Y, and Z is (e-(x+y+z) f(x, y, z) 0 < x, 0 < y, 0 <z elsewhere (a) (3 pts) Verify that the joint density function is a valid density function. (b) (3 pts) Find the joint marginal density function of X and Y alone (by integrating over 2). (C) (4 pts) Find the marginal density functions for X and Y. (d) (3 pts) What are P(1 < X <...
The table below gives the joint probability mass function of a pair of discrete random variables X and Y. Pxr(x,y) 12 3 P) 10.30 0.05 0.15 2 0.10 0.05 0.35 px(x) Complete the marginal distributions in the table above. . Are X and Y independent? Yes Check
1) Suppose that three random variables, X, Y, and Z have a continuous joint probability density function f(x, y. z) elsewhere a) Determine the value of the constant b) Find the marginal joint p. d. fof X and Y, namely f(x, y) (3 Points) c) Using part b), compute the conditional probability of Z given X and Y. That is, find f (Z I x y) d) Using the result from part c), compute P(Z<0.5 x - 3 Points) 2...