Question

consider the discrete random variable x given in the table below calculate the mean variance and standard deviation of eggs also calculate the expected value of x around solution to three decimal places if necessary

Answer 1

The mean and the expected value are computed as follows:

`\mu=\sum ^{}_{}x_i\cdot P(x_i)`

Substituting with data:

`\begin{gathered} \mu=1\cdot0.07+6\cdot0.07+11\cdot0.08+15\cdot0.09+18\cdot0.69 \\ \mu=0.07+0.42+0.88+1.35+12.42 \\ \mu=15.14 \\ E(x)=15.14 \end{gathered}`

The variance is calculated as follows:

`\sigma^2=(x_i-\mu)^2\cdot P(x_i_{})`

Substituting with data:

And the standard deviation is the square root of the variance, that is:

`\begin{gathered} \sigma=\sqrt[]{\sigma^2} \\ \sigma=\sqrt[]{26.8604} \\ \sigma=5.183 \end{gathered}`