A common probability density has the form:

P(x) = Ae^(−x/x0), 0 < x < ∞

where A and x0 are constants.

a) If x0 is specified, what then must the value of A be in order
for P(x) to be normalized?

b) Calculate < x >, the average value of x.

c) Find x1 such that the probability of observing x between 0 and
x1 is one half. What is the value of P(x1)?

d) Sketch P(x), labeling x0 and x1.

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