Thread: Beta Distribution

Hi,

I'm trying to work out P(Y≥0.9) for Y~Beta(4,1).
I did P(Y≥0.9) = 1- P(Y≤0.9)
= 1 - (5-1)!/(4-1)! * (0.9^3) * (1-0.9)^0
= 1 - 2.916 = -1.916

But this is obviously wrong! I can't see where i have gone wrong.

Thanks for any help.

Originally Posted by blacksheep

Hi,

I'm trying to work out P(Y≥0.9) for Y~Beta(4,1).
I did P(Y≥0.9) = 1- P(Y≤0.9)
= 1 - (5-1)!/(4-1)! * (0.9^3) * (1-0.9)^0
= 1 - 2.916 = -1.916

But this is obviously wrong! I can't see where i have gone wrong.

Thanks for any help.

I am not sure what you did, but given Y~Beta(4,1), I would use the Beta pdf of Y to solve.

$\displaystyle P(Y\geq\\0.9)=\frac{\Gamma(4+1)}{\Gamma(4)\Gamma(1 )}\int_{0.9}^{1}y^{4-1}(1-y)^{1-1}dy
$