Question

The table below shows the probability distribution of a random variable X. X P(X) --20 0.39 -19 0.02 -18 0.18 0.22 -16 0.1 -15 0.09 What is the mean of the probability distribution? Write your answer as a decimal.

Answer 1

-18.11

Step-by-step explanation

We want to find the mean of the probability distribution.

To do that, we apply the formula:

`\mu=\Sigma\mleft\lbrace X\cdot P(X)\mright\rbrace`

This means that we have to find the product of each value has its corresonding probability and find the sum:

`\begin{gathered} \mu=(-20\cdot0.39)+(-19\cdot0.02)+(-18\cdot0.18)+(-17\cdot0.22)+(-16\cdot0.1)+(-15\cdot0.09) \\ \mu=(-7.8)+(-0.38)+(-3.24)+(-3.74)+(-1.6)+(-1.35) \\ \mu=-18.11 \end{gathered}`

That is the mean of the probability distribution.