The random variables ? and ? have the following joint pdf. ??,? (?, ?) = ??...

The random variables ? and ? have the following joint pdf. ??,? (?, ?) = ?? ^-8x^{^2-18y^2}

a) Find the mean and variance of ? and ? and the value of ?.

b) Determine if ? and ? are independent.

c) Determine the distribution of ? and ?.

Expert Solution

ANSWER::

NOTE:: I HOPE THIS ANSWER IS HELPFULL TO YOU......**PLEASE SUPPORT ME WITH YOUR RATING......

**PLEASE GIVE ME "LIKE".....ITS VERY IMPORTANT FOR,ME......PLEASE SUPPORT ME .......THANK YOU

orchestra answered 2 years ago

The joint pdf of a two continuous random variables is given as follows: ??,? (?, ?)...

The joint pdf of a two continuous random variables is given as follows: ??,? (?, ?) = { ??? 0 < ? < 2, 0 < ? < 1 0 ??ℎ?????? 1) Find c. 2) Find the marginal PDFs of ? and ?. Make sure to write the ranges. Are these random variables independent? 3) Find ?(0 < ? < 1|0 < ? < 1) 4) What is ??|? (?|?). Make sure to write the range of ?.

Suppose A and B are independent uniform random variables on [0,1]. What is the joint PDF...

Suppose A and B are independent uniform random variables on [0,1]. What is the joint PDF of (R,S)? Prove that R and S are are independent standard normal random variables. R = sqrt(-2logA)*cos(2piB) S = sqrt(-2logA)*sin(2piB)

Suppose A and B are independent uniform random variables on [0,1]. What is the joint PDF...

Suppose A and B are independent uniform random variables on [0,1]. What is the joint PDF of (R,S)? Prove that R and S are are independent standard normal random variables. R = sqrt(-2logA)*cos(2piB) S = sqrt(-2logA)*sin(2piB)

(i) Find the marginal probability distributions for the random variables X1 and X2 with joint pdf...

(i) Find the marginal probability distributions for the random variables X1 and X2 with joint pdf f(x1, x2) = 12x1x2(1-x2) , 0 < x1 <1 0 < x2 < 1 , otherwise (ii) Calculate E(X1) and E(X2) (iii) Are the variables X1 and X2 stochastically independent? (iv) Given the variables in the question, find the conditional p.d.f. of X1 given 0<x2< ½ and the conditional expectation E[X1|0<x2< ½ ].

The joint probability density function (PDF) of two random variables (X,Y) is given by ???(?,?) =...

The joint probability density function (PDF) of two random variables (X,Y) is given by ???(?,?) = { 1, 0 ≤ ? ≤ 2,0 ≤ ? ≤ 1,2? ≤ ? 0, otherwise 1) Find the correlation coefficient ??? between the two random variables X and Y Find the probability P(Y>X/2). help please asap

Suppose that Y1 and Y2 are random variables with joint pdf given by f(y1,y2) = ky1y2...

Suppose that Y1 and Y2 are random variables with joint pdf given by f(y1,y2) = ky1y2 ; 0 < y1 <y2 <1, where k is a constant equal to 8. a) Find the conditional expected value and variance of Y1 given Y2=y2. b) Are Y1 and Y2 independent? Justify your answer. c) Find the covariance and correlation between Y1 and Y2. d) Find the expected value and variance of Y1+Y2.

Let X and Y be independent Exponential random variables with common mean 1. Their joint pdf...

Let X and Y be independent Exponential random variables with common mean 1. Their joint pdf is f(x,y) = exp (-x-y) for x > 0 and y > 0 , f(x, y ) = 0 otherwise. (See "Independence" on page 349) Let U = min(X, Y) and V = max (X, Y). The joint pdf of U and V is f(u, v) = 2 exp (-u-v) for 0 < u < v < infinity, f(u, v ) = 0 otherwise....

The continuous random variables ? and ? have the joint p.d.f. ??,? given by ?(?, ?)...

The continuous random variables ? and ? have the joint p.d.f. ??,? given by ?(?, ?) = { ?^ (−?−?) , ? > 0, ? > 0 0 otherwise a) Find the conditional p.d.f. ??|?(?|?) of ? given ? = ?. [1] b) Find ?(?|? = ?) and ???(?|? = ?). [1] c) Find ?(?) and ???(?). [1] d) Find ???(?, ?). [1]

Let X and Y be continuous random variables with joint pdf f(x, y) = kxy^2 0...

Let X and Y be continuous random variables with joint pdf f(x, y) = kxy^2 0 < x, 0 < y, x + y < 2 and 0 otherwise 1) Find P[X ≥ 1|Y ≤ 1.5] 2) Find P[X ≥ 0.5|Y ≤ 1]

Let X1, X2, X3 be continuous random variables with joint pdf f(X1, X2, X3)= 2 if...

Let X1, X2, X3 be continuous random variables with joint pdf f(X1, X2, X3)= 2 if 1<X1<2 -1<X2<0 -X2-1<X3<0 0 otherwise Find Cov(X2, X3)

Question

The random variables ? and ? have the following joint pdf. ??,? (?, ?) = ??...

Solutions

Expert Solution

Related Solutions

The joint pdf of a two continuous random variables is given as follows: ??,? (?, ?)...

Suppose A and B are independent uniform random variables on [0,1]. What is the joint PDF...

Suppose A and B are independent uniform random variables on [0,1]. What is the joint PDF...

(i) Find the marginal probability distributions for the random variables X1 and X2 with joint pdf...

The joint probability density function (PDF) of two random variables (X,Y) is given by ???(?,?) =...

Suppose that Y1 and Y2 are random variables with joint pdf given by f(y1,y2) = ky1y2...

Let X and Y be independent Exponential random variables with common mean 1. Their joint pdf...

The continuous random variables ? and ? have the joint p.d.f. ??,? given by ?(?, ?)...

Let X and Y be continuous random variables with joint pdf f(x, y) = kxy^2 0...

Let X1, X2, X3 be continuous random variables with joint pdf f(X1, X2, X3)= 2 if...