InterviewSolution
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InterviewSolution
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The probability distribution of a discrete random variable x is given as under Calculate (i) the value of A, if E(X)=2.94. (ii) variance of X. |
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Answer» (i) We have,`sumXP(X)=1/2+2/5+12/25+(2A)/10+(3A)/25+(5A)/25` `=(25+20+24+10A+6A+10A)/50=(69+26A)/50` Since, E(X)=`sumXP(X)` `rArr2.94=(69+26A)/50` `rArr 26A=50xx2.94-69` `rArrA=(147-69)/26=78/26=3` (ii) We know that, Var(X)=`E(X^(2))-[E(X)]^(2)` `=sumX^(2)P(X)-[sumXP(X)]^(2)` `=1/2+4/5+48/25+(4A^(2))/10+(9A^(2))/25+(25A^(2))/25-[E(X)]^(2)` `=(20+40+96+20A^(2)+18A^(2)+50A^(2))/50-[E(X)]^(2)` `=(161+88A^(2))/50-[E(C)]^(2)=(161+88xx(3)^(2))/50-[E(X)]^(2)` `[becauseA=3]` `=953/50-[2.94]^(2)` [`becauseE(X)=2.94`] =19.0600-8.6436=10.4164 |
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