Math 419
REVIEW
Random Variables
Problem Set 3
Math 419
Random Variables
Problem Set 3
Math 419
Random Variables
Problem Set 3
1. An insurance policy pays an individual 100 per day for up to 3 days of hospitalization and 25 per day
of hospitalization thereafter. The number of days of hospitalization X is a discrete random variable
with probability function
f(x) = (6 – x) / 15 , for x = 1, 2, 3, 4, 5
0 ,
otherwise
Calculate the expected payment for hospitalization under this policy.
Math 419
Random Variables
Problem Set 3
2. Let X be a random variable with the following distribution. Calculate the coefficient of variation of
X.
x
P( X = x )
13
0.14
17
0.25
26
0.09
31
0.11
45
0.25
49
0.16
Math 419
Random Variables
Problem Set 3
3. An unfair coin is tossed. If it is heads, a die with the property that getting any even number is twice
as likely as getting any odd number is rolled. If the coin lands tails, then a fair die is rolled.
Let X be any number on the upper face of the die, and let F be the cumulative distribution of X. If
F(3) = 0.472, find F(4).
Math 419
Random Variables
Problem Set 3
4. The following table gives the probabilities of events for random variables X and Y. Find the standard
deviation of 2Y – X.
Y
_|__ 0________200_________400_____
|
0 | 0.95
0.01
0.009
|
X 200 | 0.009
0.008
0.006
|
400 | 0.007
0.0007
0.0003
|
|