8. (a) A discrete random variable X has probability mass function defined by c(10 - z), for 1 = 1, 2 f(z) =c(18 - ), for z = 3, 4 0, otherwise %3D Find (i) the value of the constant c, (ii) the median...

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Extracted text: 8. (a) A discrete random variable X has probability mass function defined by c(10 - z), for 1 = 1, 2 f(z) =c(18 - ), for z = 3, 4 0, otherwise %3D Find (i) the value of the constant c, (ii) the median of X, (iii) the mean and standard deviation of X. (b) A continuous random variable Y has normal distribution with mean 4 and variance 1. Given that P(Y > k) = 0.025, determine the value of k.