Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

Login

Username

Password

Not registered yet?

#1 2012-10-31 05:14:59

genericname
Full Member

Offline

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
Moderator

Offline

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
 

#3 2012-10-31 06:16:16

genericname
Full Member

Offline

Re: Question about geometric series

Thank you, bob.

 

Board footer

Powered by FluxBB