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

  1. Apr 11, 2013 #1
    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
     
  2. jcsd
  3. Apr 12, 2013 #2

    HallsofIvy

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    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?

    It hard to believe your textbook does not tell how to find expectation!
     
  4. Apr 12, 2013 #3

    Ray Vickson

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    Your probabilities are incorrect: their sum is 0.3 + 0.4 + 0.6 + 0.1 = 1.4. Perhaps you made a simple typo.
     
  5. Apr 12, 2013 #4

    haruspex

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