We rolling two fair dice (at the same time), and consider [N, A=22,P] the probability space...

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We rolling two fair dice (at the same time), and consider [N, A=22,P] the probability space of this random experiment. Now, if X is a map defined on 2 as follow: - 3 if = (i, j) with i = 2, 3, 4, 5, 6 and j<i if (i, j) with j = 2, 3, 4, 5, 6 and i < j otherwise X (0) = +2 0 a) Prove that X is a random variable on [N, A = 2°, P]. b) Determine the probability mass function P(x = •). c. Calculate the mean and standard deviation for the random variable X. We rolling two fair dice (at the same time), and consider [N, A=22,P] the probability space of this random experiment. Now, if X is a map defined on 2 as follow: - 3 if = (i, j) with i = 2, 3, 4, 5, 6 and j<i if (i, j) with j = 2, 3, 4, 5, 6 and i < j otherwise X (0) = +2 0 a) Prove that X is a random variable on [N, A = 2°, P]. b) Determine the probability mass function P(x = •). c. Calculate the mean and standard deviation for the random variable X.