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The random variable X represents the volatility of stocks in the S&P 500. The pdf of...

The random variable X represents the volatility of stocks in the S&P 500. The pdf of X is suspected to have the form:

f(x) = 4cxe^-(cx)^2, x > 0

Determine the value(s) of c so that the above function a valid probability density function

Solutions

Expert Solution

c = 2

EXPLANATION:

Given function:

Value of c is found by noting that the Total Ptobability = 1.

Thus Total Probability is given by:

(1)

Substitute

(2)

So, we get:

So, (1) becomes:

(3)

Substituting (2), equation (3) becomes:

between lilits 0 to .

Applying limits, we get:

TotalProbability = 1

Thus, we get:

So,

c = 2

milcah answered 1 month ago

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