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# 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

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