Suppose that x has a let a distribution with parameters a 1

Suppose that x has a let a distribution with parameters a = 1 and b = 4.2, determine the following P(x

Solution

a=1

b=4.2

a).

p( x < 0.25) = 0.7013

b). p( 0.5< x) =0.0544

c).

f(x) = B(a,b)^-1x^a-1 (1-x)^b-1    for 0 < x < 1

f(0.192307692308) = 2.120490445895

Expectation = a/(a + b) = 0.192307692308

Variance = ab /[(a + b + 1) (a + b)²] = 0.025052490933

Standard deviation = 0.158279786876