Part (a): The following table givesthe probability distribution of the random va

Question

Part (a):

The following table givesthe probability distribution of the random variable X, the numberof foreign tours a minister make in a year.

X

1

2

3

4

5

P(X)

0.1

0.2

0.3

0.3

0.1

Find the probabilitythat:

i) Minister makes visitbetween 2 and 5 (both exclusive)

ii) Minister makes at themost 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)

X

1

2

3

4

5

P(X)

0.1

0.2

0.3

0.3

0.1

Explanation / Answer

i) Minister makes visit between 2 and 5 (both exclusive)

P(2<X<5)=P(X=3)+P(X=4)=0.3+0.3=0.6

ii) Minister makes at the most 4 tours

P(X<=4)=1-P(X=5)=1-0.1=0.9

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)

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