The following questions are taken from the book 'Modern Engineering Mathematics' by Glyn James.
Q.35 (p. 895) The distribution of the number X of independent attempts needed to achieve the first success when the probability of success 0.2 at each attempt is given by
P(X = k) = (0.2)(0.8)^(k-1) (k = 1, 2, 3, ...)
Find the mean, the median and the standard deviation for this distribution.
Q. 45 (p. 896)
In a problem similar to that in Question 35 the probability of success at the first attempt is 0.2 but the probability of failure at each subsequent attempt (if needed) is half that for the previous attempt. Find the mean number of attempts needed to achieve the first success.
I have attempted to interpret this question at the following page, but it appears to have led to confusion:
How can I calculate the mean number of attempts needed for success?
What is the method and answer for Question 45 please?