Help with random variables and expectations
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Help with random variables and expectations

[From: ] [author: ] [Date: 11-09-05] [Hit: ]
2] and f(x) = 0 otherwise.is a constant to be determined by you.(b) The density function for X is given by: f(x) = bx^2 for x is the set [0, 2] and f(x) = 0 otherwise. Here B is a constant to be determined by you.(c) Find V ar(X) for both part a) & b).......
Let X be a random variable which is de…fined over the interval [0, 2]. Find E[X], E[X^2], and E[ 1/
X ] for the following scenarios:
(a) The density function for X is given by: f(x) = ax for x is the set [0, 2] and f(x) = 0 otherwise. Here A
is a constant to be determined by you.
(b) The density function for X is given by: f(x) = bx^2 for x is the set [0, 2] and f(x) = 0 otherwise. Here B is a constant to be determined by you.
(c) Find V ar(X) for both part a) & b).

I dont know where to start. Help please

-
a) Integral(0,2) ax dx = 1 gives
a[x^2/2](0,2) = 1
2a = 1
a = 1/2

E(X) = Integral(0,2) (1/2)x^2 dx = (1/2)[x^3/3](0,2) = 8/6
E(X^2) = Integral(0,2) (1/2)x^3 dx = (1/2)[x^4/4](0,2) = 2
V(X) = E(X^2) - [E(X)]^2 = 2 - (8/6)^2 = 0.2222
1
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