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We are given the following probability distribution. x 0 1 2 3 PIX] .4 .3 .2 .1 a. Calculate the mean, variance, and standard deviation. b. Suppose that Y = 3X + 2. For each value of X, determine the value of Y. What is the probability distribution of Y? c. Calculate the mean, variance, and standard devi ation from the probability distribution of 1'. (1. Use the laws of expected value and variance to calculate the mean, variance, and standard devi- ation of Y from the mean, variance, and stan- dard deviation of X. Compare your answers in parts (c) and (d). Are they the same (except for rounding)