Random variables - Exercise set 2

This exercise set contains some solved exercises on absolutely continuous random variables and probability density functions. The theory needed to solve these exercises is introduced in the lecture entitled Random variables.

Exercise 2.1

Let be an absolutely continuous random variable. Let its support be:

Let its probability density function be: [eq3]

Compute:

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The probability that an absolutely continuous random variable takes a value in a given interval is equal to the integral of the probability density function over that interval: [eq5]

Exercise 2.2

Let be an absolutely continuous random variable. Let its support be:

Let its probability density function be: [eq8]

Compute:

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The probability that an absolutely continuous random variable takes a value in a given interval is equal to the integral of the probability density function over that interval: [eq10]

Exercise 2.3

Let be an absolutely continuous random variable. Let its support be:

Let its probability density function be: [eq13] where $\lambda >0$ .

Compute:

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The probability that an absolutely continuous random variable takes a value in a given interval is equal to the integral of the probability density function over that interval: [eq15]

by Marco Taboga

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