Answered: 2. If the density of a random variable… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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2. If the density of a random variable R is zero for x¢ the finite interval [a, b],
show that NR(s) is finite for all s.

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Suppose that X, Y , and Z are random variables with a joint density f(x, y, z) = ( 6/((1+x+y+z)^4)) , when x, y, z > 0, and 0, otherwise. Determine the distribution of X + Y + Z.
Suppose the joint probability density of X and Y is fX,Y (x, y) = 3y 2 with 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 and zero everywhere else. 1. Compute E[X|Y = y]. 2. Compute E[X3 + X|X < .5]
If X is a continuous random variable with a density that is symmetric aboutsome point, ξ , show that E(X) = ξ , provided that E(X) exists.
Suppose that the random variables X and Y have a joint density function given by: f(x,y) = {c(2x+y) for 2≤x≤6 and 0≤y≤5, 0 otherwise P(3 < X < 5, Y >1), P(X < 3), P(X +Y > 5), Find the joint distribution function (cdf),
Suppose that X is a continuous random variable with density function f(x). If f(x)=k for −5≤x≤3 and f(x)=0 otherwise, determine the value of k.
Suppose that the random variables X and Y have a joint density function given by: f(x,y)={cxy for 0≤x≤2 and 0≤y≤x, 0 otherwise c=1/2 P(X < 1), Determine whether X and Y are independent
If the joint density of X and Y is given byf(x, y) =⎧⎨⎩e−(x+y) for x > 0, y > 00 elsewhere and Z = X + Y2 , find the probability density of Z by thedistribution function technique.
Let X and Y be a pair of continuous random variables with a joint density fx,y(x,y). Assume that fx,y(x,y) = cxy for x greater than or equal to 0, y greater than or equal to 0, and x + y less than or equal to 1. Here c is a constant. Assume that fx,y(x,y) is 0 elsewhere. What is the constant c equal to? With the value of c, what is E[XY]?
Determine k so thatf(x, y) = kx(x − y) for 0 < x < 1, −x < y < x0 elsewherecan serve as a joint probability density.
If the joint probability density of X and Y is given byf(x, y) = 24xy for 0 < x < 1, 0 < y < 1, x + y < 10 elsewhere find P(X + Y < 12 ).
Suppose that the random variables X,Y, and Z have the joint probability density function f(x,y,z) = 8xyz for 0<x<1, 0<y<1, and 0<z<1. Determine P(X<0.7).

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