Alex wants to log in his online banking accounts He tries un

Alex wants to log in his online banking accounts. He tries until he remembers the correct password or until he enters four passwords, whichever comes first. Find the expected number of correct and incorrect passwords that Alex enters. (Assume that the probability of entering a correct password is ½ (each time), and it is assumed that these two events are independent.)

Solution

Sol)

Alex wants to log in his online banking accounts. He tries until he remembers the correct password or until he enters four passwords, whichever comes first. Find the expected number of correct and incorrect passwords that Alex enters.

Here X follows geometric distribution.

with p=0.5 and q=0.5 and n=4

The pmf of geometric distribution is

p(x) = p*q^x-1

p(4) =(0.5)*(0.5)^4-1

P(4)=0.063

expected number of correct and incorrect passwords is (1-p)/p = q/p = 0.5 /0.5 =1