[Q2] The sample space of a random experiment is {a, b, c, d, e, f}, and...

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[Q2] The sample space of a random experiment is {a, b, c, d, e, f}, and each outcome is equally likely. A random variable is defined as follows: outcome X i. ii. iii. iv. с d 111111 a 0 b 0 1.5 e 2 Determine the probability mass function of X. Determine the cumulative distribution function of the random variable Use the probability mass function to determine the following probabilities: (a) P(X= 1.5) (c) P(X> 3) (e) P(X = 0 or X = 2) Calculate the mean and variance of the random variable (b) P(0.5 < X < 2.7) (d) P(0 ≤X <2) [Q2] The sample space of a random experiment is {a, b, c, d, e, f}, and each outcome is equally likely. A random variable is defined as follows: outcome X i. ii. iii. iv. с d 111111 a 0 b 0 1.5 e 2 Determine the probability mass function of X. Determine the cumulative distribution function of the random variable Use the probability mass function to determine the following probabilities: (a) P(X= 1.5) (c) P(X> 3) (e) P(X = 0 or X = 2) Calculate the mean and variance of the random variable (b) P(0.5 < X < 2.7) (d) P(0 ≤X <2)