Question

question number 4. (10.00 points) suppose you have a distribution, x, with mean = 18 and standard deviation = 6. define a new random variable y = 6x - 2. find the mean and standard deviation of y. o ey = 106; σy = 36 o ey = 108; σy = 216 o ey = 108; σy = 34 o ey = 106; σy = 216 o ey = 106; σy = 34 none of the above

Explanation:

Step1: Recall mean - transformation formula

For a linear transformation \(Y = aX + b\), the mean \(E[Y]=aE[X]+b\). Given \(X\) has mean \(E[X]=18\), \(a = 6\) and \(b=- 2\). Then \(E[Y]=6\times18-2\).
\[E[Y]=108 - 2=106\]

Step2: Recall standard - deviation transformation formula

For a linear transformation \(Y=aX + b\), the standard deviation \(\sigma_Y=\vert a\vert\sigma_X\). Given \(\sigma_X = 6\) and \(a = 6\), then \(\sigma_Y=6\times6 = 36\)

Answer:

E[Y]=106; \(\sigma_Y = 36\)