Question

In: Statistics and Probability

Given the joint density function of X and Y as fX,Y(x,y) = cx2 + xy/3 0...

Given the joint density function of X and Y as fX,Y(x,y) = cx2 + xy/3

0 <x <1 and 0 < y < 2.

complete work shading appropriate regions for all integral calculations.

Find the expected value of Z = e(s1X+s2Y) where s1 and s2 are any constants.

Solutions

Expert Solution

please rate me high.


Related Solutions

The joint probability density function for two random variables X and Y is given as, fx,y...
The joint probability density function for two random variables X and Y is given as, fx,y (x, y) = (2/3)(1 + 2xy3 ), 0 < x < 1, 0 < y < 1 (a) Find the marginal probability density functions for X and Y . (b) Are X and Y independent? Justify your answer. (c) Show that E[X] = 4/9 and E[Y ] = 7/15 . (d) Calculate Cov(X, Y )
Given the joint probability density function f(x ,y )=k (xy+ 1) for 0<x <1--and--0<y<1 , find...
Given the joint probability density function f(x ,y )=k (xy+ 1) for 0<x <1--and--0<y<1 , find the correlation--ROW p (X,Y) .
. Let X and Y be a random variables with the joint probability density function fX,Y...
. Let X and Y be a random variables with the joint probability density function fX,Y (x, y) = { 1, 0 < x, y < 1 0, otherwise } . a. Let W = max(X, Y ) Compute the probability density function of W. b. Let U = min(X, Y ) Compute the probability density function of U. c. Compute the probability density function of X + Y ..
Suppose that the joint probability density function of ˜ (X, Y) is given by:´ f X,Y...
Suppose that the joint probability density function of ˜ (X, Y) is given by:´ f X,Y (x,y) = 4x/y3 I(0.1)(x), I (1, ∞)(y). Calculate a) P(1/2 < X < 3/4, 0 < Y ≤ 1/3). b) P(Y > 5). c) P(Y > X).
Let (X, Y) be a random vector with a function of the joint density given by...
Let (X, Y) be a random vector with a function of the joint density given by ˜ fX, Y (x, y) = k (2x + y) I (2,6) (x) I (0.5) (y) a) Determine k so that f X, Y (x, y) is a true probability density function joint quality. b) Determine the marginal probability density functions of X and Y. c) Calculate P (3 <X <4, Y> 2). d) Calculate P (X + Y> 4).
If the joint probability density function of the random variables X and Y is given by...
If the joint probability density function of the random variables X and Y is given by f(x, y) = (1/4)(x + 2y) for 0 < x < 2, 0 < y < 1, 0 elsewhere (a) Find the conditional density of Y given X = x, and use it to evaluate P (X + Y/2 ≥ 1 | X = 1/2) (b) Find the conditional mean and the conditional variance of Y given X = 1/2 (c) Find the variance...
Let (X, Y) be a random vector with a function of the joint density given by...
Let (X, Y) be a random vector with a function of the joint density given by ˜ fX, Y (x, y) = k (2x + y) I (2,6) (x) I (0.5) (y) a) Determine k so that f X, Y (x, y) is a true probability density function joint quality. b) Determine the marginal probability density functions of X and Y. c) Calculate P (3 <X <4, Y> 2). d) Calculate P (X + Y> 4).
The (mixed) random variable X has probability density function (pdf) fX (x) given by: fx(x)=0.5δ(x−3)+ {...
The (mixed) random variable X has probability density function (pdf) fX (x) given by: fx(x)=0.5δ(x−3)+ { c.(4-x2), 0≤x≤2 0, otherwise where c is a constant. (a) Sketch fX (x) and find the constant c. (b) Find P (X > 1). (c) Suppose that somebody tells you {X > 1} occurred. Find the conditional pdf fX|{X>1}(x), the pdf of X given that {X > 1}. (d) Find FX(x), the cumulative distribution function of X. (e) Let Y = X2 . Find...
1. Let X be a random variable with probability density function fX given by fX(x) =...
1. Let X be a random variable with probability density function fX given by fX(x) = γαγ/ (x + α)^γ+1 , x ≥ 0, 0, x < 0, where α > 0 and γ > 0. (a) Find the cumulative distribution function (cdf) FX of X. (b) Let Y = log(X+α /α) . Find the cdf of Y and identify the distribution. (c) How could a realisation of X be generated from an R(0,1) random number generator? (d) Let Z...
4. The joint density function of (X, Y ) is f(x,y)=2(x+y), 0≤y≤x≤1 . Find the correlation...
4. The joint density function of (X, Y ) is f(x,y)=2(x+y), 0≤y≤x≤1 . Find the correlation coefficient ρX,Y . 5. The height of female students in KU follows a normal distribution with mean 165.3 cm and s.d. 7.3cm. The height of male students in KU follows a normal distribution with mean 175.2 cm and s.d. 9.2cm. What is the probability that a random female student is taller than a male student in KU?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT