Pure Mathematics
Statistics

Worked Example 5

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

Hence find the mode of [latex]X[/latex].

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