Question

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

Answer 1

Hint: We first express the expectations as the means for the probability distribution. We use the formula of the mean of $E\left( X \right)=\sum{X.P\left( X \right)}$. We put the values from the chart to find the mean. It serves as the measure of central tendency of the probability distribution.

Complete step by step solution:
The mean of a probability distribution is the long-run arithmetic average value of a random variable having that distribution. If the random variable is denoted by, then it is also known as the expected value of (denoted).
We have been provided with the events and their probability distribution.
We apply the formula for mean for probability distribution.
If $E\left( X \right)$ be the means of the probability distribution then we can say that $E\left( X \right)=\sum{X.P\left( X \right)}$.
Now we have the all required values ewe put them in the formula to get
$\begin{align}
  & E\left( X \right)=\sum{X.P\left( X \right)} \\
 & \Rightarrow E\left( X \right)=1\times 0.2+2\times 0.1+3\times 0.35+4\times 0.05+5\times 0.3 \\
\end{align}$
We complete the multiplications to get
$\begin{align}
  & E\left( X \right)=1\times 0.2+2\times 0.1+3\times 0.35+4\times 0.05+5\times 0.3 \\
 & \Rightarrow E\left( X \right)=0.2+0.2+1.05+0.2+1.5=3.15 \\
\end{align}$

Note:
A binomial distribution represents the results from a simple experiment where there is “success” or “failure.” For example, if you are polling voters to see who is voting Democrat, the voters that say they will vote Democrat is a “success” and anything else is a failure.