The PDF of the two independent random variables X and Y are shown in the image below. fx(x) fy(y) 1/2 1/2 -1 -2 -1 Suppose Z = X+Y. Determine the probability density value at z = 0, fz(0).

help please answer in text form with proper workings and explanation for each and every part and steps with concept and introduction no AI no copy paste remember answer must be in proper format with all working

Say what will be the expected value of the momentum (px) of a particle described by the wave function

Q. 3 Let continuous random variables X and Y be independent identically distributed random variables with the following respective pdfs: fx(x) = 2e-2x;x 2 0 and fy (y) = 2e-2y;y > 0 Define a new random variable Z = X + Y. Derive moment generating function of Z, i.e. Mz(t).