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Let `X~B(n,p)`, if E(X)=5,Var(X)`=2.5` then `P(X lt 1)` is equal toA. `((1)/(2))^(11)`B. `((1)/(2))^(10)`C. `((1)/(2)))^(6)`D. `((1)/(2))^(9)` |
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Answer» Correct Answer - B Given mean E(x)=5 and variance, Var(X)=2.5 `therefore np=5 and npq=2.5` `Rightarrow 5q=2.5=q=(1)/(2)` Also, p+q=1 `therefore p=1-(1)/(2)=(1)/(2)` `therefore np=5` `Rightarrow np=5` `Rightarrow n xx(1)/(2)=5 " "[therefore p=(1)/(2)]` `Rightarrow n=10` `p(X lt 1)==p(X=0)=""^(n)C_(r) p^(r) q^(n-r)` `=""^(10)C_(0) ((1)/(2))^(0) ((1)/(2))^(10-0)` `=1xx 1xx((1)/(2))^(10)=((1)/(2))^(10)` |
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