You only need to do Q2 (a)'s (i) and (ii). No need to do part B...

Question

Question

2. (a) Let X be a random variable with a continuous distribution F.

(i) Show that the Random Variable Y = F(X) is uniformly distributed over (0,1). (Hint: Al- though F is the distribution of X,

You only need to do Q2 (a)'s (i) and (ii). No need to do part B

Answer 1

Answer #1

- i dit à be an randem variable with a continuous df f. Then show that F (2) vucol. 12es z u So since is a distribution fenet

Answer 2

Similar Homework Help Questions

I am studying Continuous Random Variables. Hope can some one tell me the solutions of these two problems! II.1 Let X be...

I am studying Continuous Random Variables. Hope can some one tell me the solutions of these two problems! II.1 Let X be a continuous random variable with the density function 1/4 if x E (-2,2) 0 otherwise &Cx)={ Find the probability density function of Z = X density function fx. Find the distribution function Fy (t) and the density function f,(t) of Y=지 (in terms of Fx and fx). II.1 Let X be a continuous random variable with the density...
1. Let X and Y be two jointly continuous random variables with joint CDF otherwsie a....

1. Let X and Y be two jointly continuous random variables with joint CDF otherwsie a. Find the joint pdf fxy(x, y), marginal pdf (fx(x) and fy()) and cdf (Fx(x) and Fy)) b. Find the conditional pdf fxiy Cr ly c. Find the probability P(X < Y = y) d. Are X and Y independent?
Problem # 8. a) Let X be a continuous random variable with known CDF FX(x). LetY = g(X) where g(·) is the so-called sign...

Problem # 8. a) Let X be a continuous random variable with known CDF FX(x). LetY = g(X) where g(·) is the so-called signum function, which extracts the sign of its argument. In other words, g(X) = { -1 x<0, 0 x=0, 1 x>0 } Express the PDF fY (y) in terms of the known CDF FX(x). b) Let X be a random variable with PDF: fX(x) = { x/2 0 <= x < 2, 0 otherwise} Let Y be...

(a) Let X be a continuous random variable with the cdf F(x) and pdf f(.1). Find...

(a) Let X be a continuous random variable with the cdf F(x) and pdf f(.1). Find the cdf and pdf of |X|. (b) Let Z ~ N(0,1), find the cdf and pdf of |Z| (express the cdf using ” (-), the cdf of Z; give the explicit formula for the pdf).
X is a positive continuous random variable with density fX(x). Y = ln(X). Find the cumulative...

X is a positive continuous random variable with density fX(x). Y = ln(X). Find the cumulative distribution function (cdf) Fy(y) of Y in terms of the cdf of X. Find the probability density function (pdf) fy(y) of Y in terms of the pdf of X. For the remaining problem (problem 3 (3),(4) and (5)), suppose X is a uniform random the interval (0,5). Compute the cdf and pdf of X. Compute the expectation and variance of X. What is Fy(y)?...
I only need help on quesiton 2. However, you need 1 to solve 2. Thanks :)...

I only need help on quesiton 2. However, you need 1 to solve 2. Thanks :) Q1. The random variable X has the following CDF 0 Fs(z) = 0.7, 0 z<1 (a) Draw a graph of the CDF (b) Write out the PMF of X. (c) Find out E[] (d) Find out PxIB(z), where B = {Ixl > o). what are EXIB] and VarlX1B)? Q2. Given the random variable in Q1. Let V-g(x)-지. (a) Find the PMF of V. (b)...

STAT 115 Let X be a continuous random variable having the CDF Fx(x) = 1 -...

STAT 115 Let X be a continuous random variable having the CDF Fx(x) = 1 - e^ (-e^x) (1) Find the Probability Density Function (PDF) of Y=e^X. (2) Let B have a uniform distribution over (0,1). Find a function G(b) and G(B) has the same distribution as X.
For a random variable X with cumulative distribution function (cdf) Fx(x) = 1- (2/x)^2 ,x>2. (a).Find...

For a random variable X with cumulative distribution function (cdf) Fx(x) = 1- (2/x)^2 ,x>2. (a).Find the pdf fX(x). (b).Consider the random variable Y = X^2. Find the pdf of Y, fY (y).
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

P7 continuous random variable X has the probability density function fx(x) = 2/9 if P.5 The...

P7 continuous random variable X has the probability density function fx(x) = 2/9 if P.5 The absolutely continuous random 0<r<3 and 0 elsewhere). Let (1 - if 0<x< 1, g(x) = (- 1)3 if 1<x<3, elsewhere. Calculate the pdf of Y = 9(X). P. 6 The absolutely continuous random variables X and Y have the joint probability density function fx.ya, y) = 1/(x?y?) if x > 1,y > 1 (and 0 elsewhere). Calculate the joint pdf of U = XY...