Question

Suppose you roll a pair of fair, six-sided dice until you get doubles. Let T = the number of rolls it takes. Show that T is a geometric random variable (check the BITS)

Short answer

All of the prerequisites for a geometric random variable are met. $T$is a geometric random variable as a result.

Step-by-step solution

Given Information

Given that there are two pairs of dice that are being rolled to get doubles.

The variable T shows the number of rolls dice take.

Explanation

The variable at random Because $T$is a geometric random variable,

1. Rolling a double and not rolling a double are the two successes and failures.
2. Dice rolls are not independent of one another.
3. Dice are rolled till the total is doubled.
4. The probability of rolling is predetermined.