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. Find P(0 < X <2 |Y = 0), P(X ≤ 2 |Y = 1), and P(X = 1 |Y = 1).

5. Find E(Y |X = 1) and Var(Y |X = 1).

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. 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

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)

Define the joint pmf of (X, Y) by f(0, 10) = f(0, 20) = 1 /...

Define the joint pmf of (X, Y) by f(0, 10) = f(0, 20) = 1 / 24, f(1, 10) = f(1, 30) = 1 / 24, f(1, 20) = 6 / 24, f(2, 30) = 14 / 24 Find the value of the following. Give your answer to three decimal places. a) E(Y | X = 0) = b) E(Y | X = 1) = c) E(Y | X = 2) = d) E(Y) =

Let X and Y have joint PDF f(x) = c(e^-(x/λ + y/μ)) 0 < x <...

Let X and Y have joint PDF f(x) = c(e^-(x/λ + y/μ)) 0 < x < infinity and 0 < y < infinity with parameters λ > 0 and μ > 0 a) Find c such that this is a PDF. b) Show that X and Y are Independent c) What is P(1 < X < 2, 0 < Y < 5) ? Leave in exponential form d) Find the marginal distribution of Y, f(y) e) Find E(Y)

A joint pdf is defined as f(x) =cxy for x in [1,2] and y in [4,5]...

A joint pdf is defined as f(x) =cxy for x in [1,2] and y in [4,5] (a) What is the value of the constant c? (b) Are X and Y independent? Explain. (c) What is the covariance oc X and Y? i.e. Cov(X ,Y)

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).

Let X and Y have the joint pdf f(x, y) = 8xy, 0 ≤ x ≤...

Let X and Y have the joint pdf f(x, y) = 8xy, 0 ≤ x ≤ y ≤ 1. (i) Find the conditional means of X given Y, and Y given X. (ii) Find the conditional variance of X given Y. (iii) Find the correlation coefficient between X and Y.

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

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

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