Measurements are made on the length and width (in cm) of a rectangular component

Chapter 2, Problem 15

(choose chapter or problem)

Measurements are made on the length and width (in cm) of a rectangular component. Because of measurement error, the measurements are random variables. Let X denote the length measurement and let Y denote the width measurement. Assume that the probability density function of X is

\(f(x)= \begin{cases}10 & 9.95<x<10.05 \\ 0 & \text { otherwise }\end{cases}\)

And that the probability density function of Y is

\(g(y)= \begin{cases}5 & 4.9<y<5.1 \\ 0 & \text { otherwise }\end{cases}\)

Assume that the measurements \(X \text { and } Y\) are independent.

a. Find \(P(X<9.98)\).

b. Find \(P(Y>5.01)\)

c. Find \(P(X<9.98 \text { and } Y>5.01)\).

d. Find \(\mu_{x}\).

e. Find \(\mu_{Y}\).

Equation Transcription:

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Text Transcription:

f(x)= 10 & 9.95<x<10.05 \\ 0 otherwise

g(y)= 5 & 4.9<y<5.1 \\ 0 otherwise

X and Y

P(X < 9.98)  

P(Y>5.01)  

P(X<9.98 and Y>5.01)  

\mu_x

\mu_Y