A random variable X takes values between 4 and 6 with a probability density functionf (x) =1 x ln(1.5) for 4 x 6 and f (x) =0 elsewhere. (a) Make a sketch of the probability density function. (b) Check that the total area under the probability density function is equal to 1. (c) What is P(4.5 X 5.5)? (d) Construct and sketch the cumulative distribution function. (This problem is continued in 2.3.10 and 2.4.5.)

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