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Probability Theory

  1. Oct 23, 2005 #1
    A Question Reads: "Suppose that the random Variable X is the number of failures before the first success in a series of independent Bernoulli trials with success probability p"

    a) derive the probability mass function of X
    b) what is the probability that X < x where x is a positive integer?

    My Answers:

    a) this is fairly straight forward. Its just a geometric sequence. p(x) = p(1-p)^x x = 0,1,2....

    b) I AM STUCK ON THIS. I know that X < x is just the cumulative distribution function for this geometric sequence, but that just does not work well with this. I tried something different:

    "the number of failures untill the first sucess? P(X<x) for a geometric sequnce? that means x-1 failures in n trials? (or we could think of it as x-1 sucess in n trials if we look at a failure as a success.)
    then would it be X~binomial(n,p)"

    Or perhaps it means P(X=0) + P (X=1) + P(X=2) + P(X=3).... + P(X=x-1) for a geometric sequence?

    Can somebody help me on it please? thanks!
    Last edited by a moderator: Oct 23, 2005
  2. jcsd
  3. Oct 24, 2005 #2
    I just found out now that my a) is wrong :( my prof said its not geometric, but is close to it.... anybody have any ideas?
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