Properties of the expected value - Exercise set 1

This exercise set contains some solved exercises on the properties of the expected value operator. The theory needed to solve these exercises is introduced in the lecture entitled Properties of the expected value.

Exercise 1.1

Let and be two random variables, having expected values:

Compute the expected value of the random variable defined as follows:

Solution

Exercise 1.2

Let be a random vector such that its two entries and have expected values:

Let be the following matrix of constants:

Compute the expected value of the random vector defined as follows:

Solution

Exercise 1.3

Let be a matrix with random entries, such that all its entries have expected value equal to . Let be the following constant vector:Compute the expected value of the random vector defined as follows:

Solution