已知随机变量 $X$ 服从二项分布 $X \sim B(n, p)$, 若 $E(X)=\frac{5}{4}, D(X)=\frac{15}{16}$,则 $p=(\quad)$

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答案:A

【解析】由题意 $\left\{\begin{array}{l}n p=\frac{5}{4} \\ n p(1-p)=\frac{15}{16}\end{array}\right.$, 解得 $\left\{\begin{array}{l}p=\frac{1}{4} \\ n=5\end{array}\right.$, 故选 A.