alegerrajj3030 alegerrajj3030
  • 14-08-2020
  • Mathematics
contestada

SupposeX1andX2are independent with Γ(α,1) and Γ(α+12,1) distributions. LetY= 2√X1X2.FindEYandvar(Y).

Respuesta :

Chimara
Chimara Chimara
  • 17-08-2020

Answer:

E(Y) = √a + √(a+12)

Step-by-step explanation:

X1 and X2 are independent variables while Y is the dependent variable, such that

Y = f(X1, X2)

Meaning Y is a function of X1 and X2

In this case,

Y = 2√X1X2

When (X1, X2) = (a, 1) ; Y = 2√a

When (X1, X2) = (a+12, 1) ; Y = 2√a+12

The expected value of Y is

[2√a + 2√a+12] ÷ 2  = √a + √a+12

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