Let the random variable X denote a measurement from a

QUESTION:

Let the random variable \(X\) denote a measurement from a manufactured product. Suppose that the target value for the measurement is \(m\). For example, \(X\) could denote a dimensional length, and the target might be 10 millimeters. The quality loss of the process producing the product is defined to be the expected value of \(k(X-m)^{2}\) , where k is a constant that relates a deviation from target to a loss measured in dollars.

(a) Suppose that \(X\) is a continuous random variable with \(\mathrm{E}(\mathrm{X})=\mathrm{m} \text { and } \mathrm{V}(\mathrm{X})=\sigma^{2}\).  What is the quality loss of the process?

(b) Suppose that \(X\) is a continuous random variable with

\(\mathrm{E}(\mathrm{X})=\mu \text { and } \mathrm{V}(\mathrm{X})=\sigma^{2}\). What is the quality loss of the process?

Equation Transcription:

Text Transcription:

X

m

X

k(X-m)2

X

E(X)=m and V(X)=\sigma^ 2

E(X)= and V(X)=\sigma^ 2