Suppose the random variable X has PDF fX(x) = 3x2 when 0 < x < 1...

Question

Question

Suppose the random variable X has PDF

fX(x) = 3x² when 0 < x < 1 and zero otherwise. What is the PDF of Y = 2X+3?

a.Use the general method: Find the CDF of X and use it to get the PDF of Y

b.Use a short-cut.

Answer 1

Answer #1

Answer 2

Similar Homework Help Questions

2. A continuous random variable X has PDF SPI? 1€ (-2,2] fx() = 0 otherwise (a)...

2. A continuous random variable X has PDF SPI? 1€ (-2,2] fx() = 0 otherwise (a) Find the CDF Fx (x). (b) Suppose 2 =9(X), where gle) = { " Find the (DF, PDF of
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given...

2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)
The random variable X has the following pdf: 2x 0 < x < 1 fx(x) =...

The random variable X has the following pdf: 2x 0 < x < 1 fx(x) = 0 otherwise Find the s-transform of X, Mx(s) Select one: e-s 1 O a. My(s) = - + S s2 е 1 O b. My(s) = + S 52 52 O c. 1x6) = 2 (6 + 5) O d. 1 My(s) = 2 »=2(+1)

Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the rand...

Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI <x3) Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI
The PDF of random variable X and the conditionalPDF of random variable Y given X are...

The PDF of random variable X and the conditionalPDF of random variable Y given X are fX(x) = 3x2 0≤ x ≤1, 0 otherwise, fY|X(y|x) = 2y/x2 0≤ y ≤ x,0 < x ≤ 1, 0 otherwise. (1) What is the probability model for X and Y? Find fX,Y (x, y). (2) If X = 1/2, nd the conditional PDF fY|X(y|1/2). (3) If Y = 1/2, what is the conditional PDF fX|Y (x|1/2)? (4) If Y = 1/2, what is...
4. Suppose that X and Y have the following joint PDF: e-(z+y) fx,Y(x,y) = :x>0, y...

4. Suppose that X and Y have the following joint PDF: e-(z+y) fx,Y(x,y) = :x>0, y > 0 : otherwise Use the CDF method to find and identify the distribution of WX

Suppose the random variable X has probability density function (pdf) - { -1 < x<1 otherwise...

Suppose the random variable X has probability density function (pdf) - { -1 < x<1 otherwise C fx (x) C0 : where c is a constant. (a) Show that c = 1/7; (b) Graph fx (х); (c) Given that all of the moments exist, why are all the odd moments of X zero? (d) What is the median of the distribution of X? (e) Find E (X2) and hence var X; (f) Let X1, fx (x) What is the limiting...
Suppose X is an exponential random variable with PDF, fx(x) exp(-x)u(x). Find a transformation, Y g(X) so tha...

Suppose X is an exponential random variable with PDF, fx(x) exp(-x)u(x). Find a transformation, Y g(X) so that the new random variable Y has a Cauchy PDF given 1/π . Hint: Use the results of Exercise 4.44. ) Suppose a random variable has some PDF given by ). Find a function g(x) such that Y g(x) is a uniform random variable over the interval (0, 1). Next, suppose that X is a uniform random variable. Find a function g(x) such...
For a continuous random variable X with the following probability density function (PDF): fX(x) = (...

For a continuous random variable X with the following probability density function (PDF): fX(x) = ( 0.25 if 0 ≤ x ≤ 4, 0 otherwise. (a) Sketch-out the function and confirm it’s a valid PDF. (5 points) (b) Find the CDF of X and sketch it out. (5 points) (c) Find P [ 0.5 < X ≤ 1.5 ]. (5 points)

Let X be a continuous random variable with PDF f(x) = { 3x^3 0<=x<=1 0 otherwise...

Let X be a continuous random variable with PDF f(x) = { 3x^3 0<=x<=1 0 otherwise Find CDF of X FInd pdf of Y