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Homework Help: Probability Theory - Expected Value.

  1. Oct 8, 2005 #1
    Hey.. im having some problems with this homework question, i thought perphaps somebody can help me on it.

    -- Let X be a random variable with probability mass function
    x P(x)
    -1 p
    1 1 - p

    Find the value of the constant C not equal to 1 such that E[c^X] = 1
    ------------------

    So this is my work so far. We have E[X] = 1 -2p and E[c^X] = 1 ...

    E[X] = 1 -2p
    E[c^X] = 1


    then c^X = c^(1-2p) = 1 so...

    c^(1-2p) = 1

    I do the logarithms....

    (1-2p)logc = log1
    (1-2p)logc = 0
    log c = 0
    c = 1

    but that is no true, since c cannot equal 1. What am i doing wrong?

    The only other solution i can see is 1^(1-2p)^-1 = 1/(1-2p)
     
  2. jcsd
  3. Oct 8, 2005 #2
    sorry.. the mass funtion looks awkward above... its actually...

    x p(x)
    -1 p
    1 p-1
     
  4. Oct 8, 2005 #3

    HallsofIvy

    User Avatar
    Science Advisor

    You seem to have a completely wrong idea about what's going on here!
    No, c^X is not c^(1-2p). That would be cE(x) which is irrelevant.

    What your probability function says is that x can have one of only two values: -1 and 1, with probabililty p and 1-p respectively. That means that c^x can have one of only two values: c-1= 1/c and c, with probability p and 1-p respectively. The "expected value" is the sum of the each possible value times its probability: p/c+ c(1-p)= 1. Solve that for c in terms of p.
     
  5. Oct 9, 2005 #4
    Hey... I see the error I made now....
    for solving... i managed to simplyfy the equation to 0 = (1-p)c^2 - c + p

    This is the same as... 0 = (1-p)x^2 - x + p and the idea is to solve for x or p. Believe me, I tried EVERYYTHING to solve this, even the quadratic. I just keep finding my self at a ded end. I know that c=1 works just fine, but the question says that c cannot equal to one.
    Anybody have any ideas?
     
  6. Oct 9, 2005 #5
    Ive been stuck on this for the whole day... how on earth do i solve for c?

    (1-p)C^2 - C + p = 0 //or// p/C + C(1-p) = 1

    I just keep getting 1 as an answer and the questions says C not equal to 1
     
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