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There are 5 cards numbered 1 to 5 , one number on one number on one card . Two cards are drawn at random without replacement . Let X denotes the sum of the numbers on two cards drawn . Find the mean and variance of X. |
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Answer» SOLUTION :Here, S={(1,2),(2,1),(1,3),(3,1),(2,3),(3,2),(1,4),(4,1),(1,5),(5,1),(2,4),(4,2),(2,5),(5,2),(3,4),(4,3),(3,5),(5,3),(5,4),(4,5)} `rArrn(S)=20` Let RANDOM variable variable be X which denotes the sum of the numbers on two cards DRAWN. X=3,4,5,6,7,8,9 At X=3,P(X)=`2/20=1/10` At X=4,P(X)`=2/10=1/10` At X =5,P(X)=`4/20=1/5` At X=6, P(X)=`4/20=1/5` At X=7,P(X)=`4/20=1/5` At X=8, P(X)=`2/20=1/10` At X=9,P(X)=`2/20=1/10` `THEREFORE` Mean,E(X)=`SigmaXP(X)=3/10+4/10+5/5+6/5+7/5+8/10+9/10` =`(3+4+10+12+14+8+9)/10=6` Also,`SigmaX^(2)P(X)=9/10+16/10+25/5+36/5+49/5+64/10+81/10` `=(9+16+50+72+98+64+81)/10=39` `therefore` Var(X)=`SigmaX^(2)P(X)-[SigmaXP(X)]^(2)` `=39-(6)^(2)=39-36=3` |
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