If for a binomial distribution P (X = 1) = P (X = 2) = α, write P (X= 4) in terms of α.

Given:

P (X = 1) = P (X = 2) = α

P (X= 4)=?

P(x=r)= ^{n}C_{r} p^{r} q^{n-r}

P(x=1)= ^{n}C_{1} p^{1} q^{n-1}

=npq^{n-1 (1)}

P(x=2)= ^{n}C_{2} p^{2} q^{n-2}

^{(2)}

Equating both equations ,we have:

2q = (n-1) p

4q^{2} = (n-1)^{2} p^{2}

P(x=4)= ^{n}C_{4} p^{4} q^{n-4}

For large n; n

0

So,

1