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Science · Advanced Physics
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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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