Question

In: Statistics and Probability

A random variable X has a density given by f X ( x ) = (1...

A random variable X has a density given by

f _X ( x ) = (1 − x^2 ) [ u ( x ) − u ( x − 1) ] + aδ ( x − 2 )where u(x) is the unit step function and δ(x) is a delta function.

a). Find the value of a, E(X) and σ δ_x^2 .
b). Find and make a labeled sketch of F_X (x) .

C). W = the event {X ≥ 0.5}. Find fX (x |W)and E(X |W), carefully indicating the domain

of all functions where needed.

Expert Solution

The property of Delta function is and .

Given the pdf

.

a) The property of CDF is

b) The cumulative distribution function is

The plot of is given below.

c) The conditional distribution

Thge conditional expectation,

orchestra answered 1 year ago

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