What are the expected value and variance of the following probability distribution? RANDOM VARIABLE X PROBABILITY
1 0.05
2 0.05
3 0.10
4 0.10
5 0.15
6 0.15
7 0.25
8 0.15

Expected value: 5.45

Variance: 4.0475

Step-by-step explanation:

The variance is the second moment minus the first moment squared

the first moment is just the mean

if I interpretted your table correctly the expected value (or first moment should be)

1*.05+2*.05+3*.1+4*.1+5*.15+6*.15+7*.25+8*.15= 5.45

Calculating the second moment is kind of the same thing (just square the nonprobability numbers)

1²*.05+2²*.05+3²*.1+4²*.1+5²*.15+6²*.15+7²*.25+8²*.15= 33.75

33.75-5.45²=4.0475