Question

Fill out the table and determine the value of the following quantities, Using the following p.m.f.

f(x)= (x+1)²/91, x=0,1,2,3,4,5

i.Probability Table:

x	f(x)	xf(x)
0
1
2
3
4
5

ii . What is the E[X]?

iii. What is the E[x²]?

iv.  What is Var(x)?

Answer 1

SOLUTION:

From given data,

Fill out the table and determine the value of the following quantities, Using the following p.m.f.

f(x)= (x+1)²/91, x=0,1,2,3,4,5

i.Probability Table:

x	f(x)	x*f(x)	x2*f(x)
0	0.0109	0	0
1	0.0439	0.0439	0.0439
2	0.0989	0.1978	0.3956
3	0.1758	0.5274	1.5822
4	0.2747	1.0988	4.3952
5	0.3956	1.978	9.89

ii . What is the E[X]?

E[X] = x*f(x) = 0+0.0439+0.1978+0.5274+1.0988+1.978 = 3.8459

E[X] = 3.8459

iii. What is the E[x²]?

E[X²] = x²*f(x) = 0+0.0439+0.3956+1.5822+4.3952+9.89 = 16.3069

E[X²] = 16.3069

iv.  What is Var(x)?

Var(x) = E[X²] - (E[X])²

Var(x) = 16.3069 - (3.8459)²

Var(x) = 16.3069 - 14.79094681

Var(x) = 1.5159

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