Distribution Theory 2

Question 1 In each of the following scenarios, identify the distribution of the random variable X by giving the distribution and the parameter(s). Justify your answer! (a) Suppose that drilling for water in a region is successful with probability 0.03 for each hole, independently of other holes. X the number of times that water is found when 10 holes have been drilled. (b) A box contains 20 USB flash drives, and it is known that among them is one second hand flash drive which already contains data. Two flash drives are randomly taken from the box X is the number of flash drives taken which already contain data. (c) Assume that 1% of USB flash drives bought from a street corner vendor are known to be defective. One flash drive is bought from the vendor each day, and X is the number first day when the flash drive bought turns out to be defective. (d) Assume that each day of a week has the probability 0.2 of being cloudy, independently of the weather on any other day. Let X = 1 if both Monday and Tuesday are cloudy, and X = 0 otherwise. 2021