Question

Given a random permutation of the elements of the set {a,b,c,d,e}, let X equal the number...

Given a random permutation of the elements of the set {a,b,c,d,e}, let X equal the number of elements that are in their original position (as listed). The moment generating function is X is: M(t) = 44/120 + 45/120e^t + 20/120e^2t + 10/120e^3t+1/120e^5t Explain Why there is not (e^4t) term in the moment generating function of X ?

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

Homework Answers

Answer #1

Since there are exactly 5 terms which needs to be arranged. If we want to put exactly 4 out of 5 numbers in their original place, it is not at all possible. Because if 4 are at their original place, the 5th one will automatically goes it it's original place. It simply means we can't de arrange the position of exactly 1 of 5 number because to do that, we need any other place. So we can't keep exactly 4 out of 5 numbers in its original position. That's why it's probability is 0. So, there is no terms of e4t in the moment generating function of X.

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
Let ? and ? be two independent random variables with moment generating functions ?x(?) = ?t^2+2t...
Let ? and ? be two independent random variables with moment generating functions ?x(?) = ?t^2+2t and ?Y(?)=?3t^2+t . Determine the moment generating function of ? = ? + 2?. If possible, state the distribution name (and include parameter values) of the distribution of ?.
(i) If a discrete random variable X has a moment generating function MX(t) = (1/2+(e^-t+e^t)/4)^2, all...
(i) If a discrete random variable X has a moment generating function MX(t) = (1/2+(e^-t+e^t)/4)^2, all t Find the probability mass function of X. (ii) Let X and Y be two independent continuous random variables with moment generating functions MX(t)=1/sqrt(1-t) and MY(t)=1/(1-t)^3/2, t<1 Calculate E(X+Y)^2
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 )
Let X be a random variable with probability mass function P(X =1) =1/2, P(X=2)=1/3, P(X=5)=1/6 (a)...
Let X be a random variable with probability mass function P(X =1) =1/2, P(X=2)=1/3, P(X=5)=1/6 (a) Find a function g such that E[g(X)]=1/3 ln(2) + 1/6 ln(5). You answer should give at least the values g(k) for all possible values of k of X, but you can also specify g on a larger set if possible. (b) Let t be some real number. Find a function g such that E[g(X)] =1/2 e^t + 2/3 e^(2t) + 5/6 e^(5t)
Let X be a normal random variance with media 1 and variance 4. Consider a new...
Let X be a normal random variance with media 1 and variance 4. Consider a new variance A random variable T defined below: T = -1 if X < -2 T = 0 if - 2 ≤ X ≤ 0 T = 1 if x>0 Find the moment generating function of T and, from it, calculate E (T) and Var (T).
Let X denote a random variable with probability density function a. FInd the moment generating function...
Let X denote a random variable with probability density function a. FInd the moment generating function of X b If Y = 2^x, find the mean E(Y) c Show that moments E(X ^n) where n=1,4 is given by:
1. Let the random variable X denote the time (in hours) required to upgrade a computer...
1. Let the random variable X denote the time (in hours) required to upgrade a computer system. Assume that the probability density function for X is given by: p(x) = Ce^-2x for 0 < x < infinity (and p(x) = 0 otherwise). a) Find the numerical value of C that makes this a valid probability density function. b) Find the probability that it will take at most 45 minutes to upgrade a given system. c) Use the definition of the...
Let S = {A, B, C, D, E, F, G, H, I, J} be the set...
Let S = {A, B, C, D, E, F, G, H, I, J} be the set consisting of the following elements: A = N, B = 2N , C = 2P(N) , D = [0, 1), E = ∅, F = Z × Z, G = {x ∈ N|x 2 + x < 2}, H = { 2 n 3 k |n, k ∈ N}, I = R \ Q, J = R. Consider the relation ∼ on S given...
Y is a continuous random variable with a probability density function f(y)=a+by and 0<y<1. Given E(Y^2)=1/6,...
Y is a continuous random variable with a probability density function f(y)=a+by and 0<y<1. Given E(Y^2)=1/6, Find: i) a and b. ii) the moment generating function of Y. M(t)=?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT