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genericname

Member

Registered: 2012-05-16

Posts: 52

Question about geometric series

Hi, how do I prove that the sum of all the probabilities is equal to 1 for this problem?

Flip a coin until heads show, assume that the probability of heads on one flip is 4/5. We define a random variable X = the number of flips.

a) What are the possible values of X?
b) Find the probability distribution for X: give the first four values and then find a general formula for the probability that X = n
c) Prove that the sum of all probabilities is 1 using the formula for the sum of a geometric series.

My answers:
a) X=1,2,3,...,n

b)
p(1) = 4/5
p(2) = 4/25
p(3) = 4/125
p(n) = ((1/5)^n-1) * (4/5)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Question about geometric series

hi genericname

The series could continue for ever so you need the sum to infinity of a geometric series.

Here 'a' is the first term 4/5 and r is 1/5

http://www.mathsisfun.com/algebra/seque … etric.html

Bob

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genericname

Member

Registered: 2012-05-16

Posts: 52

Re: Question about geometric series

Thank you, bob.