Please!please!please!help me with this question!?

Question

the time intervals between dial-up connections to a computer center from remote terminals are exponentially distributed with a mean of 15 seconds.

Find the mean,variance,and probability distribution of the waiting time from the opening of the computer center until the fourth dial-up connection from a remote terminal.

Many Thanks!

Answer 1

EXPONENTIAL DISTRIBUTION:

[1/λ] MEAN = VARIANCE =  15 seconds

Probability of time to 4th dial-up:

P(t < 4) = λ * exp-(λ t) = 1/15 * exp -(4/15) = 0.0511 (5.11%) probability of waiting until fourth dial-up