Question

question number 4. (10.00 points) suppose you have a distribution, x, with mean = 15 and standard deviation = 6. define a new random variable y = 6x - 5. find the mean and standard deviation of y. o ey = 85; σy = 31 o ey = 85; σy = 216 o ey = 90; σy = 31 o ey = 90; σy = 216 o ey = 85; σy = 36 o none of the above

Explanation:

Step1: Recall mean - transformation formula

If \(Y = aX + b\), then \(E[Y]=aE[X]+b\). Here \(a = 6\), \(b=- 5\) and \(E[X]=15\).
\[E[Y]=6\times15-5\]
\[E[Y]=90 - 5=85\]

Step2: Recall standard - deviation transformation formula

If \(Y=aX + b\), then \(\sigma_Y=\vert a\vert\sigma_X\). Here \(a = 6\) and \(\sigma_X = 6\).
\[\sigma_Y=6\times6 = 36\]

Answer:

None of the above