X~U(0,2) Y=3X-1 Find density of Y

Question

Question

X~U(0,2)

Y=3X-1

Find density of Y

Answer 1

Answer #1

We are given here that:

$X \sim U(0,2)$

This means that:

$3X \sim U(3*0,3*2)$

$3X \sim U(0,6)$

Therefore, we get here:

$Y = 3X - 1 \sim U(-1,5)$

Therefore now the PDF for Y is given as:

$f_y(y) = \frac{1}{5 - (-1)}, -1 < x < 5$

$f_y(y) = \frac{1}{6}, -1 < x < 5$

This is the required density of Y here.

Add a comment

Answer 2

Similar Homework Help Questions

7.9 Ife- U(0,2): a. What are the density and distribution function of Y - cos(0)? b....

7.9 Ife- U(0,2): a. What are the density and distribution function of Y - cos(0)? b. What are the mean and variance of Y?
1. Suppose the joint density of X and Y is given by f(x,y) = 6e-3x-2y, if...

1. Suppose the joint density of X and Y is given by f(x,y) = 6e-3x-2y, if 0 < x < inf., 0 < y < inf, 0 elsewhere. Part A, Find P( X < 2Y) Part B, Find Cov(X,Y) Part C, Suppose X and Y have joint density given by f(x,y) = 24xy, when 0<= x <=1, 0 <= y <=1, 0 <= x+y <=1, and 0 elsewhere. Are X and Y independent or dependent random variables? why?
2) A consumer’s utility function is u(x,y)=-1/3x^3 - 1/y (a) Find the consumer’s optimal choice for...

2) A consumer’s utility function is u(x,y)=-1/3x^3 - 1/y (a) Find the consumer’s optimal choice for x as a function of income I and prices px,py.

Consider the following joint probability density function of the random variables X and Y : 3x−y...

Consider the following joint probability density function of the random variables X and Y : 3x−y , 1 < x < 3, 1 < y < 2, f(x, y) = 9 0, elsewhere. (a) Find the marginal density functions of X and Y . (b) Are X and Y independent? (c) Find P(X > 2).
Suppose X and Y have joint probability density function fX,Y(x,y)=70e?3x?7y for 0<x<y; and fX,Y(x,y)=0 otherwise. Find...

Suppose X and Y have joint probability density function fX,Y(x,y)=70e?3x?7y for 0<x<y; and fX,Y(x,y)=0 otherwise. Find E(X). (You may either use the joint density given here,
[2.5 points] If two random variables have a joint density given by, f(x, y) = k(3x...

[2.5 points] If two random variables have a joint density given by, f(x, y) = k(3x + 2y) 0 for 0 < x < 2, 0 < y < 1 elsewhere (a) Find k (b) Find the Marginal density of Y. (c) Find E(Y) (d) Find marginal density X. (e) Find the probability, P(X < 1.3). (f) Evaluate fı(x|y); (g) Evaluate fi(x|(0.75))

3. The pair of random variables X and Y is uniformly distributed on the interior of the triangle with the vertices whose coordinates are (0,0), (0,2), and (2,0) (i.e., the joint density is equal to a...

3. The pair of random variables X and Y is uniformly distributed on the interior of the triangle with the vertices whose coordinates are (0,0), (0,2), and (2,0) (i.e., the joint density is equal to a constant inside the triangle and zero outside). (a) (10 points) Find P(Y+X< 1). (b) (10 points) Find P(X = Y). (c) (10 points) Find P(Y > 1X = 1/2). 3. The pair of random variables X and Y is uniformly distributed on the interior...
consider continuous joint density function f(x,y)= (x+y)/7; 1<x<2, 1<y<3 Marginal density for Y? Select one: (2+3x)/14...

consider continuous joint density function f(x,y)= (x+y)/7; 1<x<2, 1<y<3 Marginal density for Y? Select one: (2+3x)/14 (3+2y)/7 (2+3y)/14 (3+2y)/14 consider continuous joint density function f(x,y)= (x+y)/7 ; 1<x<2, 1<y<3 P(0<x<3, 0<y<4)=? Select one: 0.5 1 0.15 0.25
j osxal, osx+y=1 Q) f(x,y) = 24xy (1) Find PC Y >a) find joint density (111)...

j osxal, osx+y=1 Q) f(x,y) = 24xy (1) Find PC Y >a) find joint density (111) Marginal density and v=x If u=xty fulu). @ f@) = x x @ EWx) ☺ find the paf of 9 = 1 - 4 oly CX Low (23) f(x, y) = 2x7 e 2x find flylx) WEG (11) Cor (x, y) u(0,0) whese Exu) where U (0,) 64 f 6) = $

(3x, The joint density function of X and Y is given by 0 Sy sxs1 f(x,...

(3x, The joint density function of X and Y is given by 0 Sy sxs1 f(x, y) = 0, otherwise. a) Use the distribution function technique to find the distribution function of W = X-Y. For 50% of the points, you may use the transformation technique, which is longer. >) Find the probability density function of W. Find the expected value E(W). )