Chapter 6, Problem T6.7SPT

To determine

To choose: The random variable which follows geometric distribution.

Answer to Problem T6.7SPT

Random variables in part b and c follow geometric distribution.

Explanation of Solution

Concept used:

If the trials are continuously repeated until a success occurs the trials are independent and the probability of success in each trial is same, then the random variable follows geometric distribution.

In part a, a dice is rolled until two 6s occurs. Here, it can be seen clearly that the trials are repeated for more than a success $\left(=\text{ 6s}\right).$ So, it is not a case of geometric distribution.

In part b, the cards are shuffled until a heart appears. In this case, the cards are shuffled until a success occurs ( $=$ heart), so it is a case of geometric distribution.

In part c, the digits are read to get a 7. Here, the digits are read repeatedly until a success occurs $\left(=\text{ 7}\right)$ , so it is a case of geometric distribution.

In part d and e, there is no constraint of first success. Here, the random variable is concerned with the number of counts of success. Hence, part d and e do not follow geometric distribution.