1.

Find the expected value ,variance and standard deviation of random variable X whose probability mass function (p.m.f.) is given below.

Answer» Mean , `E(X)=sumXP(X)`
`=1xx(1)/(5)+2xx(2)/(5)+3xx(2)/(5)`
`=(1)/(5)+(4)/(5)+(6)/(5)=(11)/(5)`
Variance `(X)=sumX^(2)P(X)-[E(X)]^(2)`
`=1^(2)xx(1)/(5)+2^(2)xx(2)/(5)+3^(2)xx(2)/(5)-((11)/(5))^(2)`
`=(1)/(5)+(8)/(5)+(18)/(5)-(121)/(25)=(27)/(5)-(121)/(25)`
`=(135-121)/(25)=(14)/(25)`
S.D `sqrt("Variance")`
`=sqrt((14)/(25))=(3*74)/(5)`
`0*748`


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