Can someone explain how to do this problem?
a)P(X<1/2 ,Y<1/4)= (x+y) dy dx =(xy+y2/2) |1/40 dx = (x/4+1/32) dx =(x2/8+x/32) |1/20
=(1/32+1/64) =3/64
b)P(X<2Y) =1-P(Y<X/2) =1 - (x+y) dy dx =1- (xy+y2/2)|x/20 dx =1- (x2/2+x2/8) dx
=1- 5x2/8 dx =1-(5x3/24)|10 =1-5/24 =19/24
Can someone explain how to do this problem? 2. Let f(t, y) — х +у, 0<x<...
Let f(x,y) = cx( 1-y), 0 < x < 2y < 1, zero elsewhere. a) Find c. b) Are X and Y independent? Why or why not? c) Find PX +Y05)
Let X be a random variable with CDF z<0 G()=/2 0 <IS2 z>2 1 Suppose Y = X2 is another random variable, find (a) P(1/2 X 3/2), (b) P(1s X< 2) (c) P(Y X) (d) P(X 2Y). (f) If Z VX, find the CDF of Z. (d) P(X+Y 3/4)
2. Let X and Y have joint density f(x.v) = \ şcy? if 0 <x< 1 and 1 <y<2, otherwise. (a) Compute the marginal probability density function of Y. If it's equal to 0 outside of some range, be sure to make this clear. (b) Set up but do not compute an integral to find P(Y < 2X).
Let X and Y have join density 6 f(x, y) =-(x + y)2, 0 < x < 1, 0 < y < 1
8), Let X and Y be continuous random variables with joint density function f(x,y)-4xy for 0 < x < y < 1 Otherwise What is the joint density of U and V Y
3 Let (X,Y) be a random vector with the pdf Se-(x+y), f(x,y) = e-(x+y) 122 (x, y) = 1 0, (x,y) E R otherwise. Find P{} <t}. In other words, find the PDF of the r.v. . Done in the class.
sint, 0<t〈π . У(0)=1, y'(0)=0
2. Let R be the region R = {(X,Y)|X2 + y2 < 2} and let (X,Y) be a pair of random variables that is distributed uniformly on this region. That is fx,y(x, y) is constant in this region and 0 elsewhere. State the sample space and find the probability that the random variable x2 + y2 is less than 1, P[X2 +Y? < 1].
#1: Use a change of variables to integrate f (x, y) = y - x over the region described by: –3 <y – 2x < 0 and 0 < 2y – x < 3.
1. Let X be a random variable with pdf f(x )-, 0 < x < 2- a) Find the cdf F(x) b) Find the mean ofX.v c) Find the variance of X. d) Find F (1.75) e) Find PG < x < +' f) Find P(X> 1). g) Find the 40th percentile.*