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## Sample Document Text

1016-351-03
Probability
In-class exercise
2010 January 19
Consider a continuous random variable with the uniform probability density function
f(x) =
braceleftBigg
1
B?A A < x < B
0 otherwise
a. Verify that f(x) is normalized, i.e., that
integraldisplay ?
??
f(x)dx = 1
b. Sketch the graph of f(x). Label the axes.
1
Consider a continuous random variable with the uniform probability density function
f(x) =
braceleftBigg
1
B?A A < x < B
0 otherwise
c. Find the cumulative distribution F(x).
d. Sketch the graph of F(x). Label the axes.
e. Calculate the expected value E(X) in terms of A and B.
f. Calculate the variance V(X) in terms of A and B.
2
...

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