Question

In: Statistics and Probability

Compute the mean and variance of the following probability distribution. x P(x) 5................................. .1..

Compute the mean and variance of the following probability distribution.

x                                        P(x)

5.................................         .1

10...............................         .3

15...............................         .2

20...............................         .4

Solutions

Expert Solution

X

P(X)

X * P(X)

X2 * P(X)

5

0.1

0.5

2.5

10

0.3

3

30

15

0.2

3

45

20

0.4

8

160
   

ΣX × P(X) = 14.5

ΣX2 × P(X) = 237.5

 

Expected value of X is,

E(X) = ΣX × P(X) = 14.5

 

Variance of X is,

Var(X) = ΣX2 × P(X) – [E(X)]2 = 237.5 – [14.5]2 = 27.25

 

Therefore, Mean and variance of the given probability distribution are,

Mean = 14.5

Variance = 27.25

Therefore, Mean and variance of the given probability distribution are,

Mean = 14.5

Variance = 27.25

Umair answered 1 year ago
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