1. (4 points) Let X be the random variable representing the number of defective parts for...

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1. (4 points) Let X be the random variable representing the number of defective parts for a machine when 3 parts are sampled from a production line and tested. The following table is the probability distribution of X. 1 2 3 0.38 0.1 0.01 x 0 P(X= a) 0.51 (a) (2 pts) Set up the mean value of X. You don't need to simplify. (b) (2 pts) Suppose the mean value E[X] = x. Set up the variance of X using the conven- tional summation notation and x. Indicate the index of the summation carefully. 1. (4 points) Let X be the random variable representing the number of defective parts for a machine when 3 parts are sampled from a production line and tested. The following table is the probability distribution of X. 1 2 3 0.38 0.1 0.01 x 0 P(X= a) 0.51 (a) (2 pts) Set up the mean value of X. You don't need to simplify. (b) (2 pts) Suppose the mean value E[X] = x. Set up the variance of X using the conven- tional summation notation and x. Indicate the index of the summation carefully.