Let X be a random variable with density function:
f(x) = x if x ∈ (0, 1]
2 − x if x ∈ (1, 2]
0 the rest
Determine the distribution and density functions of the random variables:
a) Y = X + 1;
b) Y = −1/2X;
c) Y = X^2;

An external consultant recommends that a plant installs a bank of capacitors for power factor correction. this will reduce the peak electrical demand charges by an average of 93 kw every month. the plant current pays $13 per kw in peak demand charges. the capacitor bank will include 223 kw of fixed capacitors, and 183 of variable capacitors. the fixed capacitors cost $59 per kw, and the variable capacitors will cost $65 per kw. the consultant charges 21% of the equipment costs to install the capacitors. because this project will reduce the demand for the electric utility, they are prepared to provide a one-time rebate of $42 per kw of reduced demand. what is the simple payback period for this project (in years)?