In a binomial probability distribution there are $n$ trials and the probability of success for each

Question

In a binomial probability distribution there are $n$ trials and the probability of success for each trial is $p$. If the mean is $8$ and the variance is $4.8$, find the value of $n$ and $p$. Denoting $\mathrm{P}\left( X=r \right)$ by ${{p}_{r}}$, show that $\frac{{{p}_{r+1}}}{{{p}_{r}}}=\frac{2\left( 20-r \right)}{3\left( r+1 \right)}$, where $r=0,1,2,3,.....,18,19$.

Hence find the mode of $X$.

Accepted Answer

$n=20,\ p=\frac25$; $p_{r+1}/p_r=\frac{2(20-r)}{3(r+1)}$ for $r=0,\ldots,19$; mode $=8$.

Worked Example 5

Worked Example 5

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