Let X be a random variable with MGF MX(t)=13e−t+16+12e2t. What is P(X≤1)?

Question

Question

math Statistics-And-Probability

Answer 1

Answer #1

The MGF of X is

That means

Hence,

Answer 2

Similar Homework Help Questions

3. Let X be a random variable and denote by Mx(t) its MGF. Prove that, for any t > 0, we have 3. Let X be a random variable and denote by Mx(t) its MGF. Prove that, for any t > 0, we have

3. Let X be a random variable and denote by Mx(t) its MGF. Prove that, for any t > 0, we have 3. Let X be a random variable and denote by Mx(t) its MGF. Prove that, for any t > 0, we have
3. Let X be a random variable and denote by Mx(t) its MGF. Prove that, for...

3. Let X be a random variable and denote by Mx(t) its MGF. Prove that, for any t > 0, we have P[X >Mx(t)e
The moment generating function (MGF) for a random variable X is: Mx (t) = E[e'X]. Onc...

The moment generating function (MGF) for a random variable X is: Mx (t) = E[e'X]. Onc useful property of moment generating functions is that they make it relatively casy to compute weighted sums of independent random variables: Z=aX+BY M26) - Mx(at)My (Bt). (A) Derive the MGF for a Poisson random variable X with parameter 1. (B) Let X be a Poisson random variable with parameter 1, as above, and let y be a Poisson random variable with parameter y. X...

2.4.10 A random variable Xhas its mgf given by Mx(t) e (5 - 4e')1 for t<...

2.4.10 A random variable Xhas its mgf given by Mx(t) e (5 - 4e')1 for t< 223. Evaluate P(4 or 5). Hint: What is the mgf of a geometric random vari- able?
The mgf of a random variable X has the following form: e-8t et 5 Mx(t) =...

The mgf of a random variable X has the following form: e-8t et 5 Mx(t) = 0.64 . Find ElYX). Answer:-0.2
Consider a random variable X with RX = {−1, 0, 1} and PMF P(X = −1)...

Consider a random variable X with RX = {−1, 0, 1} and PMF P(X = −1) = 1/4 , P(X = 0) = 1/2 , P(X = 1) = 1/4 . a) Determine the moment-generating function (MGF) MX(t) of X. b) Obtain the first two derivatives of the MGF to compute E[X] and Var(X). Consider a random variable X with Rx = {-1,0,1} and PMF Determine the moment-generating function (MGF) Mx(t) of X b) Obtain the first two derivatives of...

8. Let X be a continuous random variable with mgf given by It< 1 M(t)E(eX) 1...

8. Let X be a continuous random variable with mgf given by It< 1 M(t)E(eX) 1 - t2 (a) Determine the expected value of X and the variance of X [3] (b) Let X1, X2, ... be a sequence of iid random variables with the same distribution as X. Let Y X and consider what happens to Y, as n tends to oo. (i) Is it true that Y, converges in probability to 0? (Explain.) [2] (ii) Explain why Vn...
A random variable X has moment generating function (MGF) Problem 1. Mx(s) = (n-0.2 + 0.2e2")2...

A random variable X has moment generating function (MGF) Problem 1. Mx(s) = (n-0.2 + 0.2e2")2 (a) Determine what a should be. (b) Determine E[X].
Random variable X has MGF(moment generating function) gX(t) = , t < 1. Then for random...

Random variable X has MGF(moment generating function) gX(t) = , t < 1. Then for random variable Y = aX, some constant a > 0, what is the MGF for Y ? What is the mean and variance for Y ?

EXERCISES the mgf of the random variable X, find P(x < 5.23). d so that P(e...

EXERCISES the mgf of the random variable X, find P(x < 5.23). d so that P(e < X < d) = 0.95 3.3.1. If (1-2t)-6, t<½, is V3. .3.2. If X is χ2 (5), determine the constants c and and P(X < c) = 0.025.