In: Math
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
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