T6.7. Which of the following random variables is geometric?
(a) The number of times I have to roll a die to get two$6s$.
(b) The number of cards I deal from a well-shuffled deck of$52$ cards until I get a heart.
(c) The number of digits I read in a randomly selected row of the random digits table until I find a$7$.
(d) The number of $7s$in a row of$40$ random digits.
(e) The number of $6s$I get if I roll a die $10$times

To find that the given random variable is geometric or not. Since a variable operates a geometric distribution, if the number of failures before the first success then each draw is independent of the previous ones.

The random variables are geometrically verified as follows:

1. Not geometric, because the number of failures comes first, followed by the primary two successes.
2. It is not geometric because no substitution of cards is made.
3. Geometric, because it satisfies all of the geometric distribution's conditions.
4. Not geometric because the number of successes rather than the number of failures prior to rapid success is calculated.
5. Not geometric because the number of successes rather than the number of failures before the rapid success is counted. As a result, option (c) is right.

The number of digits in a number I randomly select a row from the random digits database and read it till I discover a 7