let p ( x , y )be a joint pmf of Xand Y. p ( x...

let p ( x , y )be a joint pmf of Xand Y.

p ( x , y )	y = 0	y = 1	y = 2
x = 0	.12	.10	.08
x = 1	.13	.17	.10
x = 2	.15	.15	0

(a) Find the marginal pmf's of Xand Y.

(b) Determine whether Xand Yare independent.

c) Find Correlation (X,Y)

Expert Solution

orchestra answered 1 year ago

Let the joint pmf of X and Y be defined by f (x, y) = c(x...

Let the joint pmf of X and Y be defined by f (x, y) = c(x + y), x =0, 1, 2, y = 0, 1, with y ≤ x. 1. Are X and Y independent or dependent? Why or why not? 2. Find g(x | y) and draw a figure depicting the conditional pmfs for y =0 and 1. 3. Find h(y | x) and draw a figure depicting the conditional pmfs for x = 0, 1 and2. 4....

Let the joint pmf of X and Y be defined by f (x, y) = c(x...

Let the joint pmf of X and Y be defined by f (x, y) = c(x + y), x =0, 1, 2, y = 0, 1, with y ≤ x. 1. Find g(x | y) and draw a figure depicting the conditional pmfs for y =0 and 1. 2. Find h(y | x) and draw a figure depicting the conditional pmfs for x = 0, 1 and2. 3. Find P(0 < X <2 |Y = 0), P(X ≤ 2 |Y...

Let the random variable X and Y have the joint pmf f(x, y) = , c...

Let the random variable X and Y have the joint pmf f(x, y) = , c xy 2 where x = 1, 2, 3; y = 1, 2, x + y ≤ 4 , that is, (x, y) are {(1, 1),(1, 2),(2, 1),(2, 2),(3, 1)} . (a) Find c > 0 . (b) Find μ . X (c) Find μ . Y (d) Find σ . 2 X (e) Find σ . 2 Y (f) Find Cov (X, Y )...

Let the random variable and have the joint pmf X Y f(x,y) = {x(y)^2}/c where x...

Let the random variable and have the joint pmf X Y f(x,y) = {x(y)^2}/c where x = 1, 2, 3 ; y = 1, 2, x+y<= 4, that is (x,y) are {(1,1), (1,2), (2,1), (2,2), 3,1)} (a) Find . c > 0 (b) Find . μX (c) Find . μY (d) Find . σ2 X (e) Find . σ2 Y (f) Find Cov . (X,Y ) (g) Find p , Corr . (x,y) (h) Are and X and Y independent

2. The joint pmf of ? and ? is given by ??,? (?, ?) = （x+y）/27 ???...

2. The joint pmf of ? and ? is given by ??,? (?, ?) = （x+y）/27 ??? ? = 0, 1,2; ? = 1, 2, 3, and ??,? (?, ?) = 0 otherwise. a. Find ?(?|? = ?) for all ? = 0,1, 2. b. Find ?(3 + 0.2?|? = 2).

SOLUTION REQUIRED WITH COMPLETE STEPS Let X and Y be discrete random variables, their joint pmf...

SOLUTION REQUIRED WITH COMPLETE STEPS Let X and Y be discrete random variables, their joint pmf is given as Px,y = ?(? + ? + 2)/(B + 2) for 0 ≤ X < 3, 0 ≤ Y < 3 (Where B=0) a) Find the value of ? b) Find the marginal pmf of ? and ? c) Find conditional pmf of ? given ? = 2

Let X and Y be independent geometric random variables with parameter p. Find the pmf of...

Let X and Y be independent geometric random variables with parameter p. Find the pmf of X + Y

6 The joint PMF of X and Y is given by y\x -1 0 1 -1...

6 The joint PMF of X and Y is given by y\x -1 0 1 -1 p q p 0 q 0 q 1 p q p (a) Describe the possible values of p and q. (b) Find the marginal PMFs of X and Y . (c) Find the conditional PMF of Y given X = x for x = −1, 0, 1 (d) Find the conditional expectation of Y given X = x for x = −1, 0, 1,...

Let X and Y have joint discrete distribution p(x, y) = 3 20 (.5 x )...

Let X and Y have joint discrete distribution p(x, y) = 3 20 (.5 x ) (.7 y ), x = 0, 1, 2, . . . , and y = 0, 1, 2, . . .. Find the marginal probability function P(X = x). [hint: for a geometric series X∞ n=0 arn with −1 < r < 1, r 6= 0, then X∞ n=0 arn = a 1 − r ]

Let Y1,...,Yn have common pmf, p(y)= 2p if y = -1, 1/2 - p if y...

Let Y1,...,Yn have common pmf, p(y)= 2p if y = -1, 1/2 - p if y = 0, 1/2 - p if y = 1. a.) Find a sufficient statistics for p. b.) Find the MOM estimator of p. Is it unbiased? c.) Find the MLE estimator of p. Is it unbiased? d.) Find the MSE of both estimators. Using MSE as a criterion, which estimator is better?

Question

let p ( x , y )be a joint pmf of Xand Y. p ( x...

Solutions

Expert Solution

Related Solutions

Let the joint pmf of X and Y be defined by f (x, y) = c(x...

Let the joint pmf of X and Y be defined by f (x, y) = c(x...

Let the random variable X and Y have the joint pmf f(x, y) = , c...

Let the random variable and have the joint pmf X Y f(x,y) = {x(y)^2}/c where x...

2. The joint pmf of ? and ? is given by ??,? (?, ?) = （x+y）/27 ???...

SOLUTION REQUIRED WITH COMPLETE STEPS Let X and Y be discrete random variables, their joint pmf...

Let X and Y be independent geometric random variables with parameter p. Find the pmf of...

6 The joint PMF of X and Y is given by y\x -1 0 1 -1...

Let X and Y have joint discrete distribution p(x, y) = 3 20 (.5 x )...

Let Y1,...,Yn have common pmf, p(y)= 2p if y = -1, 1/2 - p if y...