# How do you find the mean of the following probability distribution?

## X P(X) 1 0.20 2 0.10 3 0.35 4 0.05 5 0.30

Jan 21, 2017

Mean is $3.15$

#### Explanation:

Mean of a probability distribution given by

$\left[\begin{matrix}\underline{x} & \underline{P \left(x\right)} \\ 1 & 0.20 \\ 2 & 0.10 \\ 3 & 0.35 \\ 4 & 0.05 \\ 5 & 0.30\end{matrix}\right]$

is $\frac{{\sum}_{i} x P \left(x\right)}{{\sum}_{i} P \left(x\right)}$

And hence mean is

$\frac{1 \times 0.20 + 2 \times 0.10 + 3 \times 0.35 + 4 \times 0.05 + 5 \times 0.30}{0.20 + 0.10 + 0.35 + 0.05 + 0.30}$

= $\frac{0.20 + 0.20 + 1.05 + 0.20 + 1.50}{1}$

= $3.15$