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 11:22 am
Suppose X, Y, and Z are three independent normal randomvariables. X has an expected value of 4 and a standard deviation of1.3; 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
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? e) What is the probability that T is within 0.8 standard deviationsof 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 ofT? j) What is the probability that the X, Y, and Z are all less thantheir respective 90th percentiles? k) What is the probability that X + Z > 0? l) Copy your R script or any other comments for the above into thetext box here.
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? e) What is the probability that T is within 0.8 standard deviationsof 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 ofT? j) What is the probability that the X, Y, and Z are all less thantheir respective 90th percentiles? k) What is the probability that X + Z > 0? l) Copy your R script or any other comments for the above into thetext box here.