Suppose X, Y, and Z are three independent normal random variables. X has an expected value of 7 and a standard deviation of 2; Y has an expected value of -2 and a standard deviation of 4; Z has an expected value of 5 and a standard deviation of 12. Let T = 3X + 12Y - 2z Variable X Y Mean(Expected Value) -2 Standard Deviation 4 12 Coefficient 12 -2

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Suppose X, Y, and Z are three independent normal random variables. X has an expected value of 7 and a standard deviation of 2; Y has an expected value of -2 and a standard deviation of 4; Z has an expected
value of 5 and a standard deviation of 12. Let T = 3X + 12Y - 2Z
Variable
X
Y
Mean(Expected Value)
7
-2
Standard Deviation
2
4
12
Coefficient
3
12
-2
a) What is the expected value of T?
b) What is the variance of Z?
c) What is the variance of T?
d) What is the standard deviation of T?
N LO
Transcribed Image Text:Suppose X, Y, and Z are three independent normal random variables. X has an expected value of 7 and a standard deviation of 2; Y has an expected value of -2 and a standard deviation of 4; Z has an expected value of 5 and a standard deviation of 12. Let T = 3X + 12Y - 2Z Variable X Y Mean(Expected Value) 7 -2 Standard Deviation 2 4 12 Coefficient 3 12 -2 a) What is the expected value of T? b) What is the variance of Z? c) What is the variance of T? d) What is the standard deviation of T? N LO
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