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