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Example. Suppose X ∼ U[0, 1] and Y = − ln(X) (so Y > 0). Find the p.d.f. of Y . Solution. Note. This gives a convenient way to simulate exponential random variables. 32
• Calculations similar to the previous example are required whenever we want to find the distribution of a function of a random variable Example. Suppose X has p.d.f. f X (x) and Y = aX + b for constants a and b. Find the p.d.f. f Y (y) of Y . Solution. 33
Page 1 and 2: 5. Continuous Random Variables Cont
Page 3 and 4: The following properties follow fro
Page 5 and 6: Cumulative Distribution Function (c
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: Example. At a certain bank, the amo

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