Question: The mode of a continuous random variable having density is the value of for which attains its maximum. Compute the mode of in cases (a),

The mode of a continuous random variable having density is the value of for which attains its maximum. Compute the mode of in cases (a), (b), and (c) of Theoretical Exercises 5.13.

Theoretical Exercises 5.13

Use the identity of Theoretical Exercises 5.5 to derive E[X²] when X is an exponential random variable with parameter λ.

Theoretical Exercises 5.5

Use the result that for a nonnegative random variable Y,

E[Y] P{Y >t}dt

to show that for a nonnegative random variable X,

E[Y] P{Y >t}dt

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