Suppose X, Y, and Z are three independent normal random variables. X has an expected value of 4 and a standard deviation

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Suppose X Y And Z Are Three Independent Normal Random Variables X Has An Expected Value Of 4 And A Standard Deviation 1 (276.94 KiB) Viewed 28 times

Suppose X, Y, and Z are three independent normal random variables. X has an expected value of 4 and a standard deviation of 1.3; Y has an expected value of 6 and standard deviation of 0.8; Z has an expected value of -8 and a standard deviation of 0.5 Let T = 2X + 4Y+ 4Z Variable Mean(Expected Value) Standard Deviation Coefficient a) What is the probability that X > 2? b) What is the expected value of T? c) What is the variance of T? d) What is the standard deviation of T? X 4 1.3. 2 f) What is the probability that T is > 8? Y 6 0.8 4 Z -8 e) What is the probability that T is within 0.8 standard deviations of its mean? k) What is the probability that X + Z > 0? 0.5 4 g) What is the probability that T is < 6? h) What is the probability that 6 < T < 8? i) What is the 90th percentile of the distribution of T? j) What is the probability that the X, Y, and Z are all less than their respective 90th percentiles? 1) Copy your R script or any other comments for the above into the text box here.