Go back to

The site is being constantly updated, so come back to check new updates

If you find any bug or need any improvements in solution report it here

Expected Value and Variance of a Discrete Random Variable online calculator

INSTRUCTION: Use ',' or new line to separate between values

You can see a sample solution below. Enter your data to get the solution for your question

$$\displaylines{---}$$
$$\displaylines{}$$
$$x$$
$$P(x)$$
$$24$$
$$0.1$$
$$48$$
$$0.1$$
$$55$$
$$0.3$$
$$72$$
$$0.5$$
$$\displaylines{}$$
$$\displaylines{Expectation\;=\;\sum_{i=1}^{n}x_{i}P(x)_{i} \\ \\ \,=24*0.1+48*0.1+55*0.3+72*0.5 \\ \\ \,=2.4+4.8+16.5+36.0 \\ \\ \,= \mathbf{\color{Red}{59.7}} \\ \\ Variance\;=\;\sum_{i=1}^{n}P(x)_{i}(x_{i} - \mu)^{2} \\ \\ \Rightarrow 0.1*( 24 - 59.7)^{2}+0.1*( 48 - 59.7)^{2}+0.3*( 55 - 59.7)^{2}+0.5*( 72 - 59.7)^{2} \\ \\ \Rightarrow 0.1*( -35.7)^{2}+0.1*( -11.7)^{2}+0.3*( -4.7)^{2}+0.5*( 12.3)^{2} \\ \\ \Rightarrow 127.449+13.689+6.627+75.645 \\ \\ \Rightarrow 223.41000000000003 \\ \\ \sigma = \sqrt{variance} \\ \\ \Rightarrow \mathbf{\color{Red}{14.946906}} }$$