For a binomial variate X,if n=4 and P(X=4)=6 | vedclass

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(C) The probability mass function for a binomial distribution is given by $P(X=k) = { }^n C_k p^k q^{n-k}$,where $q = 1-p$.Given $n=4$,the equation is

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$\frac{6}{7}$

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(C) The probability mass function for a binomial distribution is given by $P(X=k) = { }^n C_k p^k q^{n-k}$,where $q = 1-p$.Given $n=4$,the equation is $P(X=4) = 6 P(X=2)$.Substituting the values:${ }^4 C_4 p^4 q^0 = 6 \cdot { }^4 C_2 p^2 q^2$Since ${ }^4 C_4 = 1$ and ${ }^4 C_2 = \frac{4 	imes 3}{2 	imes 1} = 6$,we have:$1 \cdot p^4 = 6 \cdot 6 \cdot p^2 q^2$$p^4 = 36 p^2 q^2$Dividing both sides by $p^2$ (assuming $p 
eq 0$):$p^2 = 36 q^2$Taking the square root of both sides:$p = 6q$Substitute $q = 1-p$:$p = 6(1-p)$$p = 6 - 6p$$7p = 6$$p = \frac{6}{7}$

For a binomial variate $X$,if $n=4$ and $P(X=4)=6 P(X=2)$,then the value of $p$ is

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