1.Let X be a random variable having density function f(x) = CX 0 <= x <= 2 0 otherwise (a) find the value of constant C (b) find P( 1/2 < x < 3/2) (c) find P( x > 1) (d) find the distribution function.
2.Let X be a random variable giving the number of aces in a random draw of 4 cards from an ordinary deck of 52 cards. construct a table showing the probability distribution of X.
3.Three reservoirs are connected by three pipes as shown in Figure 1 with hA = 100 ft, hB = 20 ft, hC = 0 ft, l1 = 1000 ft, l2 = 500 ft, l3 = 400 ft and D1 = D2 = D3 = 1 ft. Determine flow rate into or out of each reservoir if friction in each pipe is 0.02. Neglect minor losses.