If X is a binomial variable with range {0, 1, | vedclass

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(D) For a binomial distribution,the probability mass function is given by $P(X=k) = \binom{n}{k} p^k q^{n-k}$,where $n=4$ and $q=1-p$. Given $P(X=3) =

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$\frac{4}{7}$

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(D) For a binomial distribution,the probability mass function is given by $P(X=k) = \binom{n}{k} p^k q^{n-k}$,where $n=4$ and $q=1-p$. Given $P(X=3) = 3P(X=4)$,we substitute the values: $\binom{4}{3} p^3 q^1 = 3 \binom{4}{4} p^4 q^0$ $4 p^3 q = 3(1) p^4$ Since $p 
eq 0$,we can divide both sides by $p^3$: $4q = 3p$ Substitute $q = 1-p$: $4(1-p) = 3p$ $4 - 4p = 3p$ $4 = 7p$ $p = \frac{4}{7}$ Thus,the correct option is $D$.

If $X$ is a binomial variable with range $\{0, 1, 2, 3, 4\}$ and $P(X=3) = 3P(X=4)$,then the parameter $p$ of the binomial distribution is:

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