Compute the mean and variances of the following discrete probability and distribution.

Question

Compute the mean and variances of the following discrete probability distribution.

 

X                             P(x)

2                             .50

8                             .30

10                           .20

 

 

Please show work

Answer 1

mean = E[X] = 2*.5+8*.3+10*.2 = 5.4

variance = E[X²] - E[X]²

E[X²] = 4*.5+64*.3+100*.2 =41.2

Var(X) = 41.2 - 5.4² = 12.04

Answer 2

 mean = sum of x*P(x) = 2x0.50 + 8x0.30 + 10x0.20 = 5.40

variance = sum of x^2*P(x) - mean^2 = 2^2*0.50 + 8^2*0.30 + 10^2*0.20 - (5.40)^2 = 2.00 + 19.20 + 20.00 - 29.16 = 12.04

 

I hope you understand how the answer came out.

 

Lee

Answer 3

mean

= ∑x(i)P(x(i))

= 2(.5)+8(.3)+10(.2)

= 5.4

 

variance

= ∑(x(i)-mean)^2 P(x(i))

= (2-5.4)^2 (.5) + (8-5.4)^2 (.3) + (10-5.4)^2 (.2)

= 12.04