Question

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

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)?

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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