# Probability density function

## Probability density function

The length of time, in minutes, that a customer queues in a Post Office is a random variable, T, with probability density function

where c is a constant

(a) Show that the value of c is

(b) Show that the cumulative distribution function F(t) is given by

(c) Find the probability that a customer will queue for longer than 3 minutes.

A customer has been queueing for 3 minutes.

(d) Find the probability that this customer will be queueing for at least 7 minutes.

Three customers are selected at random.

(e) Find the probability that exactly 2 of them had to queue for longer than 3 minutes.

where c is a constant

(a) Show that the value of c is

(b) Show that the cumulative distribution function F(t) is given by

(c) Find the probability that a customer will queue for longer than 3 minutes.

A customer has been queueing for 3 minutes.

(d) Find the probability that this customer will be queueing for at least 7 minutes.

Three customers are selected at random.

(e) Find the probability that exactly 2 of them had to queue for longer than 3 minutes.

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