The random variable $X$ is the number of successes in $n$ independent trials of an experiment in whi

Question

The random variable $X$ is the number of successes in $n$ independent trials of an experiment in which the probability of a success at any trial is $p$. Denoting $\mathrm{P}(X=k)$ by ${{p}_{k}}$, it is given that $\frac{{{p}_{k}}}{{{p}_{k-1}}}=\frac{(n-k+1)p}{k(1-p)}$, $k=1$, $2$, …, $n$. A distribution is said to be bimodal if it has two modes. Find the least value of $n$, and the corresponding modes of $X$, given that $X$ is bimodal and that $p=\frac{18}{25}$.

Accepted Answer

$n = 24$, modes are 17 and 18

2018 ACJC MYE Q8

2018 ACJC MYE Q8

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