Ghulam Ishaq Khan Institute of Engineering Sciences and Technology (GIKI)
Faculty of Engineering Sciences (FES)
ES 202
Spring 2023
Practice Assignment 2b
CLO 2: Calculate probability mass/density function parameters, moments and
functions of random variables.
Q 1. Let X be a random variable with the following probability distribution
๐ฅ
-3
6
9
๐(๐ฅ)
1/6
1/2
1/3
Find ๐๐(๐), where ๐(๐) = (2๐ + 1)2
Q 2. A large industrial firm purchases several new word processors at the end
of each year, the exact number depending on the frequency of repairs in the
previous year. Suppose that the number of word processors, X, purchased each
year has the following probability distribution:
๐ฅ
0
1
2
3
๐(๐ฅ)
1/10
3/10
2/5
1/5
If the cost of the desired model is $1200 per unit and at the end of the year a
refund of 50๐2 dollars will be issued, how much can this firm expect to spend
on new word processors during this year?
Q3. The hospitalization period, in days, for patients following treatment for a
certain type of kidney disorder is a random variable Y = X + 4, where X has the
density function
๐(๐ฅ)={ 32
(๐ฅ+4)3 ๐ฅ <4
0 ๐๐๐ ๐๐คโ๐๐๐
Find the average number of days that a person is hospitalized following
treatment for this disorder.
Q4. Suppose that the probabilities are 0.4, 0.3, 0.2,and 0.1, respectively, that
0, 1, 2, or 3 power failures will strike a certain subdivision in any given year.
Find the mean and variance of the random variable X representing the number
of power failures striking this subdivision.
