Assume that the measurements X and Y are independent.
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
and that the probability density function of Y is
a. Find P(X < 9.98).
b. Find P(Y > 5.01).
c. Find P(X < 9.98 and Y > 5.01).
d. Find 
.
e. Find 
.
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