Finding E(2^X) from a moment-generating function

[Tomp]

Kinda urgent help! Probability function - E(2^X)??

Question A moment-generating function of X is given by M(t) = 0.3e^t + 0.4e^(2t) + 0.2e^(3t) + 0.1e^(5t)

Find the pmf of X
My solution
x f(x)
1 0.3
2 0.4
3 0.6
5 0.1

The next question asks
Calculate E(2^X)

Which I am totally unsure about
I calculated the mean as 0.22 and variance as 5.28

Can someone provide any clues on what to do to answer this?
My notes and textbook do not have any examples or notes similar to this :S
Thanks in advance

 

[HallsofIvy]

Question A moment-generating function of X is given by M(t) = 0.3e^t + 0.4e^(2t) + 0.2e^(3t) + 0.1e^(5t)

Find the pmf of X
My solution
x f(x)
1 0.3
2 0.4
3 0.6
5 0.1

The next question asks
Calculate E(2^X)

Which I am totally unsure about
I calculated the mean as 0.22 and variance as 5.28

The mean and variance of what? The problem asked just for E(2^X) which is, by definition,
2^1(0.3)+ 2^2(0.4)+ 2^3(0.6)+ 2^5(0.1).

That was using the values you give. What happened to x= 4?

Can someone provide any clues on what to do to answer this?
My notes and textbook do not have any examples or notes similar to this :S
Thanks in advance

It hard to believe your textbook does not tell how to find expectation!

 

[Ray Vickson]

Question A moment-generating function of X is given by M(t) = 0.3e^t + 0.4e^(2t) + 0.2e^(3t) + 0.1e^(5t)

Find the pmf of X
My solution
x f(x)
1 0.3
2 0.4
3 0.6
5 0.1

The next question asks
Calculate E(2^X)

Which I am totally unsure about
I calculated the mean as 0.22 and variance as 5.28

Can someone provide any clues on what to do to answer this?
My notes and textbook do not have any examples or notes similar to this :S
Thanks in advance

Your probabilities are incorrect: their sum is 0.3 + 0.4 + 0.6 + 0.1 = 1.4. Perhaps you made a simple typo.

 

[haruspex]

Suppose the pmf is P[X=r] = p_r. How would you write E[e^tX] in terms of t and the pmf? What do you get if you equate that expression to the given mgf?