Answer:
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
