a) A resident of Karen estimates that within the range of likely temperatures his April electricity bill, E, in Kenya shillings (Ksh), will be: E = 290 - 5A where: A is the average temperature for the month, in degrees Fahrenheit. If the average January temperature is represented by a random variable with a mean of 24 and a standard deviation of 4, find the mean and standard deviation of this resident’s April electricity bill.

b) The continuous random variable X has p.d.f. f(x) where f(x) =(x 3), 0≤x≤4. (i) Find E(X) (ii) Find E(2X 5) (iii) Find E(X2 ) (iv) Find E(X2 2X - 3)