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1 The random variable X has the following probability distribution {prof}: r 2 1 I] 1 2 P{X=r] 0.05 0.2 0.35 0.15 {1.25 (a) Find the corresponding cumulative distribution function (cdf) and plot its graph. (b) Find E{X}, vaer} and org. Show your working carefully. dn'E-E 2 A foursided {tetrahedral} die has a different number 1, 2, 3 or at axed to each face. On any given roll? each of the four numbers is equally likely to occur (face down]. An experiment consists of rolling the die twice and recording the two values obtained in order. Random variable X represents the greater of the two values? random variable Y represents the rst value minus the second. (a) Construct the sample space S for the experiment. (b) Construct the induced sample space SKY for (I, Y}. [c] Construct the probability distributions for X and Y. (d) Obtain #3:, y, ox, cry. [e] Ubtain Cov(X,Y) = ny. Are X and Y correlated? [f] Are I and Y independent? Justify your answer. dnrlTa