### Video Transcript

The function in a given table is a
probability function of a discrete random variable π₯. Find the expected value of π₯.

For a discrete random variable, the
expected value is worked out by finding the sum of the products of the value of the
random variable and its probability. Here, thatβs the function of
π₯. Before we can calculate the
expected value of π₯, we first need to work out the value of the unknown in the
table, π.

Since π of π₯ is a probability
function, we know the all outcomes sum to one. If we therefore subtract the given
probabilities from one, weβll get the value of π. One minus 0.1 add 0.1 add 0.4 add
0.2 is 0.2. Our value of π is therefore
0.2. Now we can calculate the expected
value of π₯.

Each part of this is given by the
product of the value of the random variable and its associated probability: zero
multiplied by 0.1 add one multiplied by 0.2 add two multiplied by 0.1 add three
multiplied by 0.4 add four multiplied by 0.2. Simplifying each parts of this sum
gives us zero add 0.2 add 0.2 add 1.2 add 0.8, which gives us 2.4. The expected value of π₯ is
therefore 2.4.