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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
Posted: Mon Jul 11, 2022 11:48 am
by answerhappygod
- Suppose X Y And Z Are Three Independent Normal Random Variables X Has An Expected Value Of 4 And A Standard Deviation 1 (40.65 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 a 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 Y Z 6 -8 0.8 0.5 4 4 e) What is the probability that T is within 0.8 standard deviations of its mean? f) What is the probability that T is > 8? 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? k) What is the probability that X + Z > 0? 1) Copy your R script or any other comments for the above into the text box here.