ein three weights, 30% weigh 5 pounds, 30% weigh 10 pounds, 40% weigh 15 pounds.

Question

ein three weights, 30% weigh 5 pounds, 30% weigh 10 pounds, 40% weigh 15 pounds. een ball at random. X and Y are independent. Let X denote the weight 3. Red balls com Green balls come in two weights, 60% weigh 8 pounds, 40% weigh 16 p Select one red ball and one gr of the red ball and let Y denote the weight of the green ball. ounds. a) Write out the joint distribution of (X,Y) as a 3 by 2 matrix of probabilities. b) Compute E(XY) nd PX-Y4), the probability the weights of the 2 balls are within 4 pounds of each other.

Explanation / Answer

a) The joint probability distribution for X, Y here is obtained as:

b) The expected value of XY is computed as:

E(XY) = 8*(5*0.18 + 10*0.18 + 15*0.24) + 16*(0.12*5 + 0.12*10 + 0.16*15 )

E(XY) = 50.4 + 67.2 = 117.6

Therefore E(XY) = 117.6

c) The required probability here is computed as:

P(| X - Y| < 4) = 0.18 + 0.18 + 0.16 = 0.52

Therefore 0.52 is the required probability here.

X = 5 X = 10 X = 15 Y = 8 0.6*0.3 = 0.18 0.6*0.3 = 0.18 0.6*0.4 = 0.24 Y = 16 0.4*0.3 = 0.12 0.4*0.3 = 0.12 0.4*0.4 = 0.16

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