Question

(a) It is given that a random variable X such that P(X =−1) =P(X = 1)...

(a) It is given that a random variable X such that P(X =−1) =P(X = 1) = 1/4, P(X = 0) = 1/2. Find the mgf of X, mX(t)

(b) Let X1 and X2 be two iid random varibles such that P(Xi =1)=P(Xi =−1)=1/2, i=1,2. Use the mgfs to prove that X and Y =(X1+X2)/2 have the same distribution

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
Consider the family of distributions with pmf pX(x) = p if x = −1, 2p if...
Consider the family of distributions with pmf pX(x) = p if x = −1, 2p if x = 0, 1 − 3p if x = 1 . Here p is an unknown parameter, and 0 ≤ p ≤ 1/3. Let X1, X2, . . . , Xn be iid with common pmf a member of this family. Consider the statistics A = the number of i with Xi = −1, B = the number of i with Xi = 0,...
If X1 and X2 are several independent random variables with distribution to the given data respectively...
If X1 and X2 are several independent random variables with distribution to the given data respectively by P(Xi = −1) = P (Xi = 1) = 1/2 , for i = 1,2, are X1 and X1X2 are independent? Justify your answer.
Suppose that X1 and X2 are independent continuous random variables with the same probability density function...
Suppose that X1 and X2 are independent continuous random variables with the same probability density function as: f(x) = ( x 2 0 < x < 2, 0 otherwise. Let a new random variable be Y = min(X1, X2,). a) Use distribution function method to find the probability density function of Y, fY (y). b) Compute P(Y > 1).
Suppose that X1 and X2 are independent continuous random variables with the same probability density function...
Suppose that X1 and X2 are independent continuous random variables with the same probability density function as: f(x) = ( x 2 0 < x < 2, 0 otherwise. Let a new random variable be Y = min(X1, X2,). a) Use distribution function method to find the probability density function of Y, fY (y). b) Compute P(Y > 1). c) Compute E(Y )
Given a random variable X following normal distribution with mean of -3 and standard deviation of...
Given a random variable X following normal distribution with mean of -3 and standard deviation of 4. Then random variable Y=0.4X+5 is also normal. (1)Find the distribution of Y, i.e. μy,σy (2)Find the probabilities P(−4<X<0),P(−1<Y<0) (3)Find the probabilities(let n size =8) P(−4<X¯<0),P(3<Y¯<4) (4)Find the 53th percentile of the distribution of X
The range of a discrete random variable X is {−1, 0, 1}. Let MX (t) be...
The range of a discrete random variable X is {−1, 0, 1}. Let MX (t) be the moment generating function of X, and let MX(1) = MX(2) = 0.5. Find the third moment of X, E(X^3).
The range of a discrete random variable X is {−1, 0, 1}. Let MX(t) be the...
The range of a discrete random variable X is {−1, 0, 1}. Let MX(t) be the moment generating function of X, and let MX(1) = MX(2) = 0.5. Find the third moment of X, E(X^3 )
Poisson Distribution: p(x, λ)  =   λx  exp(-λ) /x!  ,  x = 0, 1, 2, ….. Find the moment generating function Mx(t)...
Poisson Distribution: p(x, λ)  =   λx  exp(-λ) /x!  ,  x = 0, 1, 2, ….. Find the moment generating function Mx(t) Find E(X) using the moment generating function 2. If X1 , X2 , X3  are independent and have means 4, 9, and 3, and variencesn3, 7, and 5. Given that Y = 2X1  -  3X2  + 4X3. find the mean of Y variance of  Y. 3. A safety engineer claims that 2 in 12 automobile accidents are due to driver fatigue. Using the formula for Binomial Distribution find the...
Let P = (X1, X2) be a randomly selected point in the unit square [0, 1]...
Let P = (X1, X2) be a randomly selected point in the unit square [0, 1] 2. Let X = min(X1, X2), Y = max(X1, X2)
 (a) Find the c.d.f Fx and the density function fx, of the random variable X. (b) Find the probability P (Y − X ≤ 1/2).
Suppose a random variable X takes on the value of -1 or 1, each with the...
Suppose a random variable X takes on the value of -1 or 1, each with the probability of 1/2. Let y=X1+X2+X3+X4, where X1,....X4 are independent. Find E(Y) and Find Var(Y)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT