Discuss the below:
Q1. The probability that an experiment has a successful outcome is 0.8. The experiment is to be repeated until five successful outcomes have occurred. What is the expected number of repetitions required? What is the variance?
Q2. In a lot of 10 components, 2 are sampled at random for inspection. Assume that in fact exactly 2 of the 10 components in the lot are defective. Let X be the number of sampled components that are defective.
a. Find P(X=0).
b. Find P(X=1).
c. Find P(X=2).
d. Find the probability mass function of X.
e. Find the mean of X.
f. Find the standard deviation of X.