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:

$\begin{gathered} \sigma^2=(1-15.14)^2\cdot0.07+(6-15.14)^2\cdot0.07+(11-15.14)^2\cdot0.08+(15-15.14)^2\cdot0.09+(18-15.14)^2\cdot0.69 \\ \sigma^2=(-14.14)^2\cdot0.07+(-9.14)^2\cdot0.07+(-4.14)^2\cdot0.08+(-0.14)^2\cdot0.09+2.86^2\cdot0.69 \\ \sigma^2=199.9396\cdot0.07+83.5396\cdot0.07+17.1396\cdot0.08+0.0196\cdot0.09+8.1796\cdot0.69 \\ \sigma^2=26.860 \end{gathered}$

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

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