Answer:
(a) E(X) = 0.625
V(X) = 0.0260
(b) P(X≤0.2) = 0.00468
(c) P(0.2≤X≤0.6) =0.425
(d) The expected proportion = 0.375
Step-by-step explanation:
Given data;
α = 5
β = 3
(a) E(X) and V(X).
the mean E(X) of a beta distribution is given by the formula;
E(X) = α/(α+β)
Substituting, we have;
E(X) = 5/(5+3)
= 5/8
= 0.625
The variance V(X) of a beta distribution is given by the formula;
V(X) = αβ/(α+β)²(α+β+1)
Substituting, we have;
V(X) = 5*3/(5+3)²(5+3+1)
= 15/(8² * 9)
= 15/576
= 0.0260
See the attached file for solution to (b), (c) and (d
