Question

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

Options

• \[\frac{1}{4}\]

• \[\frac{3}{4}\]

• \[\frac{1}{3}\]

• \[\frac{4}{7}\]

Answer 1

\[\frac{4}{7}\]

Explanation:

Here n = 4

P(X = 3) = 3P(X = 4)

\[\mathrm{^4C_3p^3q=3~^4C_4p^4q^0}\]

\[\therefore\quad4\mathrm{p}^3\mathrm{q}=3\mathrm{p}^4\]

\[\therefore\quad4(1-\mathrm{p})=3\mathrm{p}\]

\[\therefore\quad4-4\mathrm{p}=3\mathrm{p}\]

\[\therefore\quad4=7\mathrm{p}\]

\[\therefore\quad\mathrm{p}=\frac{4}{7}\]