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#1 2012-10-31 05:14:59
- genericname
- Full Member
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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)
#2 2012-10-31 05:28:18
- bob bundy
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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
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei