Q. 6.7 Which of the following random va... [FREE SOLUTION]

91影视

The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 837 pages

ISBN: 9781319113339

Chapter 6: Q. 6.7 (page 437)

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

Short Answer

Expert verified

In parts b and c, random variables have a geometric distribution.

Step by step solution

Given Information

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

Explanation for correct option

The cards are shuffled in option 'b' until a heart appears. The cards are shuffled in this scenario until a success (heart) happens, hence it is a case of geometric distribution.
Option 'c' involves reading the digits to obtain a 7. It is an example of geometric distribution since the digits are read repeatedly until a success occurs $(= 7)$ .

Explanation for incorrect option

Option (a) A die is rolled until two 6s appear. It is evident here that the trials are repeated for more than a success $= 6$ . As a result, it isn't an instance of geometric distribution.
There is no first success constraint in option 'd' and 'e'. The random variable in this case is concerned with the number of counts of success. As a result, option d and e do not have a geometric distribution.