Assignment # 4 (Lessons22-27) Question 1 5+5+5=15 Marks Part (a): The following
ID: 2953008 • Letter: A
Question
Assignment # 4 (Lessons22-27)
Question 1 5+5+5=15 Marks
Part (a):
The following table gives the probability distribution of therandom variable X, the number of foreign tours a minister make in ayear.
X
1
2
3
4
5
P(X)
0.1
0.2
0.3
0.3
0.1
Find the probability that:
i) Minister makes visit between 2 and 5 (both exclusive)
ii) Minister makes at the most 4 tours
Part (b):
The range of the random variable X is [0, 1, 2, 3, x], where xis unknown. If each value is equally likely and the mean of X is 6,determine x.
Part (c):
Show that the following function satisfies the properties of ajoint probability mass function.
X Y f(x,y)
-1 -2 1/8
-0.5 -1 1/4
0.5 1 1/2
1 2 1/8
Also determine E(X) and E(Y)
Question2 3+12=15Marks
Part (a):
Discuss what is meant by the concept of independence of twodiscrete random variables.
Part (b):
Given is the joint probability distribution of X and Y.
Y
X
0
1
2
3
g(X)
0
0.05
0.05
0.10
0
0.20
1
0.05
0.10
0.25
0.10
0.50
2
0
0.15
0.10
0.05
0.30
h(Y)
0.10
0.30
0.45
0.15
1.00
Determine the followings.
I. Mean of X and Mean of Y
II. Var(X) and Var (Y)
III. Cov (X, Y)
IV. Correlation coefficientr.
- END -
X
1
2
3
4
5
P(X)
0.1
0.2
0.3
0.3
0.1
Explanation / Answer
x.