Question

The table below shows the probability distribution of a random variable Y. Y P(Y) -19 0.23 -18 0.13 -17 0.1 -16 0.04 -15 0 -14 0.5 What is the mean of the probability distribution? Write your answer as a decimal.

Answer 1

The mean (μ) of a probability distribution for a discrete variable is:

$\mu=\Sigma y\cdot P(y)$

where P(y) are the probabilities of y-values.

Substituting with the values of the table:

$\begin{gathered} \mu=-19\cdot0.23-18\cdot0.13-17\cdot0.1-16\cdot0.04-15\cdot0-14\cdot0.5 \\ \mu=-4.37-2.34-1.7-0.64-7 \\ \mu=-16.05 \end{gathered}$