1. Let X have the p.d.f fx(x) = (0 otherwise Calculate E(x) and the second central...

Question

Question

math Statistics-And-Probability

Answer 1

Answer #1

Here,

Mean of X is

$E(X) = int_{0}^{1}x*f_X(x)dx = int_{0}^{1}x*2x dx = 2 int_{0}^{1}x^2dx$

$Rightarrow E(X) = 2 int_{0}^{1}x^2dx$

$Rightarrow E(X) = 2[rac{x^3}{3}]_{0}^{1}$

Rightarrow E(X) = 2*rac{1}{3}

E(X)

The second order central moment is

$E(X-rac{2}{3})^2 = int_{0}^{1}(x-rac{2}{3})^2f_X(x)dx$

2 2 0

2 3 9 0

2 0

r4 4 2.3 42.2 3 3 9 2

413 2111

2 2 14 2 2 3 1

2 2 3 1

(ans)

Answer 2

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