The probability that a telephone call lasts no more than t minutes is often modeled as an exponential cumulative distribution function F(t)={(1-e^(-t/3), t?0,@0 otherwise.)

a) What is the probability density function of the duration in minutes of a telephone conversation?

b) What is the probability that a conversation will last between 2 and 4 minutes?

c) What is E(T), the expected duration of a telephone call?

d) What are the variance and standard deviation of T?

e) What is the probability that a call duration is within ±1 standard deviation of the expected call duration?