i need the answer quickly Joint distributions for X, Y, and Z:Y=0Y=1Y=0Y=1X=00.1250.1250.4050.045X=10.1250.1250.0450.405Z=0Z=1a) Find conditional distribution of X and Y given Z=0b) Find conditional distribution of X and Y given Z=1c) Show that X and Y are independent given Zd) Find the marginal distribution of X and Ye) Show that X and Y are not marginally independent

Joint distribution for X, Y, and Z is provided. The question's purpose is to calculate the…

Answered: Joint distributions for X, Y, and Z:…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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IF F(x, y) is the value of the joint distribution function of X and Y at (x, y), show that the marginal distribution function of X is given by G(x) = F(x, ∞) for - ∞ <x < ∞ Use this result to find the marginal distribution function of X for the random variable F(x, y) = { (1-e-x2 ) (1- e-y2) for x>0, y> 0 and 0 elsewhere
Let X and Y have the joint pdff(x,y)=cx^2y,−y≤x≤1.5,0≤y≤1.5f(x,y)=cx2y a) Determine the value of the constant cc b) Give the value of the marginal pdf fX(x)at x = -0.5 c) Give the value of the marginal cdf FX(x)at x = 0.5 d) Give the value of the conditional distribution fX|Y(x|Y=0.5) at x = 0.5
Let X,Y be i.i.d. random variables from U(0,1) distribution. (a) Give the joint distribution of X+Y and X-Y. Are they independent? Justify your answer. (b) Give the marginal distributions of X + Y and X - Y. (c) Compute E(X2 - Y).
let X be a binomial random variable with parameters n and θ1. Conditional on X = m, let Y be a binomial random variable with parametersm and θ2.(a) What is the marginal distribution of Y ?(b) Find the functions g(k) = E(Y |X = k) and v(k) = V ar(Y |X = k).Use these to find E(Y ) and V ar(Y ).(c) Find Covariance(X, Y ) and Correlation(X, Y ).
Consider X and Y are joint distributed with PDFf(x,y)=x+y, 0≤x≤1, 0≤y≤1. (d) Find the marginal distributions of X and Y .(e) Find the conditional distribution of X given Y = y.
Let X1, X2 denote two independent variables, each with a x^2(2) distribution. Find the joint pdf of Y1=X1 and Y2 = X2+X1. Note that the support of Y1, Y2 is 0<y1<y2<infinity. Also, find the marginal pdf of wach Y1 and Y2. Are Y1 and Y2 independent?
Let X1, X2, ..., Xn be a sequence of independent and identically distributedrandom variables having the Exponential(λ) distribution, λ > 0,fXi(x) = λe−λx , x > 00 , otherwise(a) Show that the moment generating function mX(s) := E(e^sX) = λ/λ−s for s < λ;(b) Using (a) find the expected value E(Xi) and the variance Var(Xi).(c) Define the random variable Y = X1 + X2 +· · ·+ Xn. Find E(Y ), Var(Y ) and the moment generating function of Y .(d) Consider a random variable X having Gamma(α, λ) distribution,fX(x) = (λαxα-1/Γ(α)) e−λx , x > 00 , otherwiseShow that the moment generating function of the random variable X is mX(s) =λα 1/(λ−s)α for s < λ, where Γ(α) isΓ(α) = (integral from 0 to inifity ) xα−1e−xdx.(e) What is the probability distribution of Y given in (c)? Explain youranswer.
Let X ~ U[0,1] and Y = -βln(1-X). What is the distribution of Y? Justify.
a) Find:i) the marginal distribution of X and Y. Are X and Y independent?ii) the probability that fewer than two children fatal given that at least one baby car seats in use at the time of the accident.b) Determine the covariance between X and Y .Give your comment on the relationship between baby car seat and child fatality.
Let Yn denote the nth order statistic of a random sample of size n froma distribution of the continuous type. Find the smallest value of n for which theinequality P(ξ0.9 < Yn) ≥ 0.75 is true.
The joint continuous distribution of random variables X and Y is given by f X,Y(x,y) = l2exp[-lx] for 0 < y < x < ∞ for some parameter l >0. = l2exp[-lx] * I[ 0 < y < x < ∞ ] Are X and Y independent? Explain. Identify the marginal distributions of X and Y by type and parameter values. Now assume that l = 3 to do the numeric computations in parts c and d. Using your findings in part b. you can simply state the means E[X] and E[Y] and variances VAR[X] and VAR[Y]. (to be used below in CORR(X,Y)) Using part b, Can you state the conditional expectation E[Y | X =x] for all possible values x of X?
Consider the pair of random variables ( X , Y ) with joint PDF f X , Y ( x , y ) = 2 for 0 ≤ x ≤ y ≤ 1 and f X , Y ( x , y ) = 0 otherwise. (In particular, note that the joint PDF is only nonzero when x ≤ y .) (a) Draw a picture of the range of ( X , Y ) in the x y -plane. (b) Describe the conditional distribution of X given Y = y , for 0 ≤ y ≤ 1 . (c) What is the marginal PDF f X of X ? (d) Are X and Y independent?

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