Question

Let random variable X ∼ U(0, 1). Let Y = a + bX, where a and...

Let random variable X ∼ U(0, 1). Let Y = a + bX, where a and b are constants.

(a) Find the distribution of Y .

(b) Find the mean and variance of Y .

(c) Find a and b so that Y ∼ U(−1, 1).

(d) Explain how to find a function (transformation), r(), so that W = r(X) has an exponential distribution with pdf f(w) = e^ −w, w > 0.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
a) Suppose that X is a uniform continuous random variable where 0 < x < 5....
a) Suppose that X is a uniform continuous random variable where 0 < x < 5. Find the pdf f(x) and use it to find P(2 < x < 3.5). b) Suppose that Y has an exponential distribution with mean 20. Find the pdf f(y) and use it to compute P(18 < Y < 23). c) Let X be a beta random variable a = 2 and b = 3. Find P(0.25 < X < 0.50)
Let X be a random variable of the mixed type having the distribution function F (...
Let X be a random variable of the mixed type having the distribution function F ( x ) = 0 w h e r e x < 0 F ( x ) = x 2 4 w h e r e 0 ≤ x < 1 F ( x ) = x + 1 4 w h e r e 1 ≤ x < 2 Question 1: Find the mean of X Question 2: Find the variance of X Question...
Let X and Y be random variable follow uniform U[0, 1]. Let Z = X to...
Let X and Y be random variable follow uniform U[0, 1]. Let Z = X to the power of Y. What is the distribution of Z?
Let X ∼ UNIF(0, 1). Find the pdf of Y = −5 ln(X) using the transformation...
Let X ∼ UNIF(0, 1). Find the pdf of Y = −5 ln(X) using the transformation technique. Note that Y is an exponential random variable. What is its parameter? Show your work.
Suppose the random variable (X, Y ) has a joint pdf for the form ?cxy 0≤x≤1,0≤y≤1...
Suppose the random variable (X, Y ) has a joint pdf for the form ?cxy 0≤x≤1,0≤y≤1 f(x,y) = . 0 elsewhere (a) (5 pts) Find c so that f is a valid distribution. (b) (6 pts) Find the marginal distribution, g(x) for X and the marginal distribution for Y , h(y). (c) (6 pts) Find P (X > Y ). (d) (6 pts) Find the pdf of X +Y. (e) (6 pts) Find P (Y < 1/2|X > 1/2). (f)...
Let X be a random variable with pdf given by fX(x) = Cx2(1−x)1(0 < x <...
Let X be a random variable with pdf given by fX(x) = Cx2(1−x)1(0 < x < 1), where C > 0 and 1(·) is the indicator function. (a) Find the value of the constant C such that fX is a valid pdf. (b) Find P(1/2 ≤ X < 1). (c) Find P(X ≤ 1/2). (d) Find P(X = 1/2). (e) Find P(1 ≤ X ≤ 2). (f) Find EX.
1. Let (X,Y ) be a pair of random variables with joint pdf given by f(x,y)...
1. Let (X,Y ) be a pair of random variables with joint pdf given by f(x,y) = 1(0 < x < 1,0 < y < 1). (a) Find P(X + Y ≤ 1). (b) Find P(|X −Y|≤ 1/2). (c) Find the joint cdf F(x,y) of (X,Y ) for all (x,y) ∈R×R. (d) Find the marginal pdf fX of X. (e) Find the marginal pdf fY of Y . (f) Find the conditional pdf f(x|y) of X|Y = y for 0...
Let X be an exponential random variable. Suppose E[X|X>a]=b, where b>a>0 are two constants. Compute the...
Let X be an exponential random variable. Suppose E[X|X>a]=b, where b>a>0 are two constants. Compute the probability P(X>a|X>a).
Let X be a random variable with pdf f(x)=12, 0<x<2. a) Find the cdf F(x). b)...
Let X be a random variable with pdf f(x)=12, 0<x<2. a) Find the cdf F(x). b) Find the mean of X. c) Find the variance of X. d) Find F (1.4). e) Find P(12<X<1). f) Find PX>3.
Let X and Y be continuous random variable with joint pdf f(x,y) = y/144 if 0...
Let X and Y be continuous random variable with joint pdf f(x,y) = y/144 if 0 < 4x < y < 12 and 0 otherwise Find Cov (X,Y).
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT