Question

The lifetime risk of developing pancreatic cancer is about one in 78 (1.28%). Let X = the number of people you ask before one says he or she has pancreatic cancer. The random variable X in this case includes only the number of trials that were failures and does not count the trial that was a success in finding a person who had the disease. X is a discrete random variable with a geometric distribution: X ~ G(178)or X ~ G(0.0128). What is the mean?

Answer 1

Mean = 1.013

Explanation:

We are given that the lifetime risk of developing pancreatic cancer is about one in 78 (1.28%).

Let X = the number of people you ask before one says he or she has pancreatic cancer.

So, in geometric distribution; X ~ Geo(p)

where p is proportion of people who does not have pancreatic cancer i.e.;

1 - 0.0128 = 0.9872

So, X ~ Geo(0.9872)

Now, the mean of geometric distribution is =
`(1)/(p)`

So, Mean of variable = (1/0.9872) = 1.013 .