STA2603 Distribution Theory II Assignment 1 Brief - Unisa

STA2603 Question 1

In each of the following scenarios,identify the distribution of the random variable X by giving the distribution and the respective parameter (s). Justify your answer! 

1. Suppose that drilling for water in a region is successful with probability 0.1 for each hole, independently of other holes. LetXbe the number of holes where water was found, out of 5 drilled holes.
2. A box contains 10 USB flash drives, and it is known that among them are five second hand flash drives which already contain data. Two flash drives are randomly chosen from the box. Xis equal to one if at least one of the flash drives chosen already contains data, otherwise X equals zero. 
3. Assume that 15% 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. Let X is the number of the day when the second defective flash drive is bought. (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 be one if both Monday and Tuesday next week are cloudy, otherwise Xis zero.

STA2603 Question 2

In each of the scenarios(a)to(d)of Question 1,calculate the probability that XD1:

STA2603 Question 3 

1. Assume that X has a uniform distribution between —3 and +3 Find the probability that X< —2 or X > 2. 
2. Assume that the percentage of medium sized businesses in Gauteng that are adequately insured has the Type I beta distribution with m= 3 and n= 3. Calculate the probability that more than 75% of medium sized businesses are adequately insured. 
3. Let X be the time in days until the next breakdown of a computer server. It is known that the distribution of Xis exponential with expected value 30 days. 
   (i) Find the median and the 90th percentile of the random variable X 
   (ii) Explain what the median and 90th percentile tell us about the time until the next break-down.