Question

use the fact that the mean of a geometric distribution is \\( \mu = \frac{1}{p} \\) and the variance is \\( \sigma^2 = \frac{q}{p^2} \\).

a daily number lottery chooses three balls numbered 0 to 9. the probability of winning the lottery is \\( \frac{1}{1000} \\). let \\( x \\) be the number of times you play the lottery before winning the first time.
(a) find the mean, variance, and standard deviation. (b) how many times would you expect to have to play the lottery before winning? it costs $1 to play and winners are paid $400. would you expect to make or lose money playing this lottery? explain.

(a) the mean is \\( \square \\). (type an integer or a decimal.)

Explanation:

Step1: Identify \( p \)

The probability of winning \( p = \frac{1}{1000} \).

Step2: Calculate the mean

Using the formula for the mean of a geometric distribution \( \mu = \frac{1}{p} \), substitute \( p = \frac{1}{1000} \). So \( \mu = \frac{1}{\frac{1}{1000}} = 1000 \).

Answer:

1000