3.14 The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with cumulative distribution function F(x) = 0, x< 0, 1 − e−8x, x ≥ 0. Find the probability of waiting less than 12 minutes between successive speeders (a) using the cumulative distribution function of X; (b) using the probability density function of X.

(a) The probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function is 0.7981.

(b) The probability of waiting less than 12 minutes between successive speeders using the probability density function is 0.7981.

Step-by-step explanation:

The  cumulative distribution function of the random variable X, the waiting time, in hours, between successive speeders spotted by a radar unit is:

(a)

Compute the probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function as follows:

The probability is:

Thus, the probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function is 0.7981.

(b)

The probability density function of X is:

Compute the probability of waiting less than 12 minutes between successive speeders using the probability density function as follows:

Thus, the probability of waiting less than 12 minutes between successive speeders using the probability density function is 0.7981.

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.