Mark the correct alternative in the following:

For a binomial variate X, if n = 3 and P (X = 1) = 8 P(X = 3), then p =

Given:

n=3

P (X = 1) = 8 P (X = 3)

P =?

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

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

=3pq^{2 (1)}

P(x=3)= ^{3}C_{3} p^{3} q^{0}

= p^{3}^{(2)}

Put values in the equations ,we have:

3pq^{2} =8 p^{3}

3 (1-p)^{2} = 8p^{2}

3+3p^{2}-6p = 6p^{2}

5p^{2}+6p-3=0

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