Respuesta :
The sum of the probabilities is always equal to 1. Summing up the probabilities given on the data set, we have
[tex]\sum P(x)=0.7+0.15+0.09+0.04+0.02=1.00[/tex]Given the probability distribution table, the mean number per inning can be computed as
[tex]\begin{gathered} \mu=(0\times0.7)+(1\times0.15)+(2\times0.09)+(3\times0.04)+(4\times0.02) \\ \mu=0.53 \end{gathered}[/tex]For the computation of the standard deviation, we need to solve first for the square of the difference of the number of innings on the mean. We have the following
[tex]\begin{gathered} (0-0.53)^2=0.2809 \\ (1-0.53)^2=0.2209 \\ (2-0.53)^2=2.1609 \\ (3-0.53)^2=6.1009 \\ (4-0.53)^2=12.0409 \end{gathered}[/tex]We then multiply these values on the corresponding probability of each inning given in the probability distribution table. We have
[tex]\begin{gathered} 0.2809\times0.7=0.19663 \\ 0.2209\times0.15=0.033135 \\ 2.1609\times0.09=0.194481 \\ 6.1009\times0.04=0.244036 \\ 12.0409\times0.02=0.240818 \end{gathered}[/tex]We now get the sum of the values computed above and get the square of it.
[tex]\begin{gathered} 0.19663+0.033135+0.194481+0.244036+0.240818 \\ \sigma=\text{ }\sqrt[]{0.9091}=0.953 \end{gathered}[/tex]