Question

1. In a box there are three numbered tickets. The numbers are 0, 1 and 2. You have to select (blindfolded) two tickets one after the other, without replacement. Define the random variable X as the number on the first ticket and the random variable Y as the sum of the numbers on your selected two tickets. E.g. if you selected first the 2 and second time 2 and Y = 1 + 2-3. the 1 , then X a./ Make a list of the possible outcomes of this experiment, with the corresponding list of X and y values and probabilities. b./ Make a joint distribution table. c./ Find the marginals and calculate E(X) and E(Y). d. Calculate Cov(X, Y). e/ Find P(X + Y 3) ard P(X + Y < 3).

Answer 1

Soluion Posible oufoms of pans amd a) Poss Corresponding vulueo of χ0md you , 3 Joint Prob distubutiom 0 3 6 2 2. PCr) 3 S imi +2+3)2

ニ(0) ( 1 ) (t) + (0) ( 2 )()+(o)(3) (0) + (1) (リは)十 (1) (2) (0) + ( ' ) ( 3)(d) 3 3 3 3 12 45 P(x) 3 3 3