consider the random variable x whose probability distributio

consider the random variable x whose probability distribution is given below

Find E(X), E(1/X), E(X^2-1), V(X)

x	1	2	3	4
P(x)	0.4	0.3	0.2	0.1

Solution

x

p

1/x

x²-1

p*X

p*1/x

p*(X²-1)

1

0.4

1

0

0.4

0.4

0

2

0.3

0.5

3

0.6

0.15

0.9

3

0.2

0.333333

8

0.6

0.066667

1.6

4

0.1

0.25

15

0.4

0.025

1.5

total

1

2

0.641667

4

E(X) = 2

E(1/X) = 0.641667

E(X²-1) = 4

X

P(X)

x*p(x)

(x-mean)²*p(x)

1

0.4

0.4

0.4

2

0.3

0.6

0

3

0.2

0.6

0.2

4

0.1

0.4

0.4

Total

1.000

2

1

V(X) =sum (x-mean)² * p(x) =1

	x	p	1/x	x2-1	p*X	p*1/x	p*(X2-1)
	1	0.4	1	0	0.4	0.4	0
	2	0.3	0.5	3	0.6	0.15	0.9
	3	0.2	0.333333	8	0.6	0.066667	1.6
	4	0.1	0.25	15	0.4	0.025	1.5
total		1			2	0.641667	4