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Discussion problem. Let X be the duration of a telephone call in minutes and suppose X has p.d.f. f(x) = c · e −x/10 for x ≥ 0. Find c, and also find the chance that the call lasts less than 5 minutes. 4
Cumulative Distribution Function (c.d.f.) • The c.d.f. of a continuous RV is defined exactly the same as for discrete RVs: F (x) = P(X ≤ x) = P (X ∈ (−∞, x]) • Hence F (x) = ∫ x f(x)dx, and differentiating −∞ both sides we get dF dx = f(x) Example. Suppose the lifetime, X, of a car battery has P(X > x) = 2 −x . Find the p.d.f. of X. 5
Page 1 and 2: 5. Continuous Random Variables Cont
Page 3: The following properties follow fro
Page 7 and 8: Example. Suppose X has p.d.f. ⎧
Page 9 and 10: Proposition 1. For X a non-negative
Page 11 and 12: Example. A stick of length 1 is spl
Page 13 and 14: The Uniform Distribution Definition
Page 15 and 16: Example. Let X ∼ U[a, b]. Show th
Page 17 and 18: Discussion problem. Suppose X ∼ U
Page 19 and 20: The Normal Distribution Definition.
Page 21 and 22: Calculating with the Normal Distrib
Page 23 and 24: Example continued. For what value o
Page 25 and 26: The Normal Approximation to the Bin
Page 27 and 28: Example. The ideal size of a first-
Page 29 and 30: Example. The amount of time, in hou
Page 31 and 32: Example. At a certain bank, the amo
Page 33 and 34: • Calculations similar to the pre

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