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"(adsbygoogle = window.adsbygoogle || []).push({});

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!

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# Probability Theory

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