# Question: Find the expected value of the random variable X whose

Find the expected value of the random variable X whose probability density is given by

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The length of certain bricks is a random variable with a mean of 8 inches and a standard deviation of 0.1 inch, and the thickness of the mortar between two bricks is a random variable with a mean of 0.5 inch and a standard ...(a) If X takes on the values 0, 1, 2, and 3 with probabilities 1/125, 12/125, 48/125 , and 64/125 , find E(X) and E(X2). (b) Use the results of part (a) to determine the value of E[(3X + 2)2]. The negative binomial distribution is sometimes defined in a different way as the distribution of the number of failures that precede the kth success. If the kth success occurs on the xth trial, it must be preceded by x – ...If the probability is f(x) that a product fails the xth time it is being used, that is, on the xth trial, then its failure rate at the xth trial is the probability that it will fail on the xth trial given that it has not ...Use repeated integration by parts to show that This result is important because values of the distribution function of a Poisson random variable may thus be obtained by referring to a table of incomplete gamma functions.Post your question