Show transcribed image text My Notes Ask Your Teac 6, -/6 points Suppose W, X, and Y are independent normal random variables with common mean $muÅŸ and known standard deviations 3,7,1 respectively. We take one observation from w, one from X and one from Y. Let S=3W-2X+5Y be a weighted sum of the three random variables. Call the realized sum s. a)Is S a normal random variable(Y/N)? b) What is the variance of S? c) What is the variance of 5S? d) What is the standard deviation of S? e) we want to test H0 :11-0 against the greater than alternative. If our test is to reject h If the realized s 45 then what is the p-value of the test? if S>40 then what is the significance eve, h test?

My Notes Ask Your Teac 6, -/6 points Suppose W, X, and Y are independent normal random variables with common mean $muÅŸ and known standard deviations 3,7,1 respectively. We take one observation from w, one from X and one from Y. Let S=3W-2X+5Y be a weighted sum of the three random variables. Call the realized sum s. a)Is S a normal random variable(Y/N)? b) What is the variance of S? c) What is the variance of 5S? d) What is the standard deviation of S? e) we want to test H0 :11-0 against the greater than alternative. If our test is to reject h If the realized s 45 then what is the p-value of the test? if S>40 then what is the significance eve, h test?