# (Solved) : Suppose X Y Independent Normal Random Variables Common Mean U Known Standard Deviations 15 Q42790506 . . .

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Suppose X, and Y are independent normal random variables with common mean u and known standard deviations 15 and 8 respectively. We take one observation from X and one from Y. Let S=4X-5Y be a weighted sum of the two random variables. Call the realized sum s. a)Is S a normal random variable(Y/N)? OY ON b) What is the variance of S? c) What is the variance of 4S? d) What is the standard deviation of S? e) We want to test Hn u-0 against the less than alternative. If our test is to reject Ho if S< -160 then what is the significance level of the test? f) If the realized s = -150, then what is the p-value of the test? g) Copy your R script for the above into the text box here This answer has not been graded yet Show transcribed image text Suppose X, and Y are independent normal random variables with common mean u and known standard deviations 15 and 8 respectively. We take one observation from X and one from Y. Let S=4X-5Y be a weighted sum of the two random variables. Call the realized sum s. a)Is S a normal random variable(Y/N)? OY ON b) What is the variance of S? c) What is the variance of 4S? d) What is the standard deviation of S? e) We want to test Hn u-0 against the less than alternative. If our test is to reject Ho if S

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