Question

Probability Density Function of beta disribution

f(y) = {10y³ (1-y) 0<y<1

0 otherwise

a) Identify the parameters for this distribution, α and β.

b) Calculate the mean and variance of Y .

c) Find the probability is better than .6, or P(Y > .6).

Answer 1

since for beta distribution:

f(x)=(1/B(α,β))*xα-1*(1-x)β-1

from above α =4 and β =2

b)

mean μ=E(X)=α/(α+β)=

2/3

variance=σ2=

αβ/((α+β)2*(α+β+1))=

2/63

c)

P(Y>0.6) = f(y) dy = 20y³(1-y) dy =20*(y⁴/4-y⁵/5)|¹_0.6 =0.6630