a)

Suppose that a continuous random variable X has MGF Mx () = (1 2) /2 where v is the parameter characterizing the distribution. (Later you will learn that this is a Chi-square distribution). . Further, suppose that Y = 2X + 1, find My (t). Please evaluate My (t = 1/10) when v = 2 to 4 decimal places. Suppose Y is the continuous random variable of the proportion of cavity magnetrons inside microwave ovens that are incorrectly installed. Then 2y, when 0