Challenging STATISTICS Question??

A student needs to know details of a class assignment that is due the next day and decides to call fellow class members for this information. She believes that for any particular call the probability of obtaining the necessary information is 0.40. She decides to continue calling class members until the information is obtained. Let the random variable X denote the number of calls needed to obtain the information.


a. Find the probability function of X.


b. Find the cumulative probability function of X.


c. Find the probability that at least three calls are required.





thanks in advance.

Challenging STATISTICS Question??
Draw up a probability tree and you can see how this works.





Let X be number of calls required to get answer.


P(x) = (0.6)^(x-1) (0.4)








Cumulative prob is found by summing a GP





CF(x) = 0.4 [ 1 + 0.6 +0.6^2 + ...]


=0.4 (sum inf of GP)


=0.4 1/(1-0.6)


=0.4/0


=1


So we do have a probability function.





P(X%26gt;=3) = 1 - P(x=1,2)


= 1 - (0.4 + 0.6x0.4)


=1 - (0.64)


= 0.36