Question

A current of I amperes flowing through a resistance of R ohms varies according to the probability distribution ? a(?)=6?(1−?),???   0<?<1;0   ??ℎ?????? and the resistance varies independently of the current according to the probability distribution ?c(?)=2?,???   0<?< 1;0   ??ℎ??????. Determine the probability distribution for the power in watts, W=I2R. Hint: Do this problem in two parts, first arguing for a distribution of I2 and taking the derivative for its density using the same argument as the proof of Theorem 3.8.2. Finish with determining the distribution of a product of independent random variables, I2 and R.

Answer 1