Part (a): The following table gives the probability distribution of therandom va
ID: 2953036 • Letter: P
Question
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.
Explanation / Answer
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)
Add up the probabilities of the Minister making 2,3, 4, or 5 visits
0.2 + 0.3 + 0.3 + 0.1 = 0.9
ii) Minister makes at the most 4 tours
Add up the probabilities the Minister makes 1, 2,3, or 4 visits
0.1 + 0.2 + 0.3 + 0.3 = 0.9