Answer:
From the values above we have the mean to be
[tex]\mu_x=1.4[/tex]
Step 1:
We will figure out the values of
[tex]x-\mu_x[/tex][tex]\begin{gathered} x-\mu_x=0-1.4=-1.4 \\ x-\mu_x=1-1.4=-0.4 \\ x-\mu_x=2-1.4=0.6 \\ x-\mu_x=3-1.4=1.6 \end{gathered}[/tex]
Step 2:
We will figure out the values of
[tex](x-\mu_x)^2[/tex][tex]\begin{gathered} (x-\mu_x)^2=(-1.4)^2=1.96 \\ (x-\mu_x)^2=(-0.4)^2=0.16 \\ (x-\mu_x)^2=(0.6)^2=0.36 \\ (x-\mu_x)^2=(1.6)^2=2.56 \end{gathered}[/tex]
Step 3:
We will figure out the value of
[tex](x-\mu_x)^2.P(x)[/tex][tex]\begin{gathered} (x-\mu_x)^2.P(x)=0.1\times1.96=0.196 \\ (x-\mu_x)^2.P(x)=0.6\times0.16=0.096 \\ (x-\mu_x)^2.P(x)=0.36\times0.1=0.036 \\ (x-\mu_x)^2.P(x)=2.56\times0.2=0.512 \end{gathered}[/tex]
Step 4:
We will calculate the variance of the distribution using the formula below
[tex]\begin{gathered} \sum_{n\mathop{=}0}^{\infty}(x-\mu_x)^2.P(x)=0.196+0.096+0.036+0.512 \\ variance=0.84 \end{gathered}[/tex]
Hence,
The variance is = 0.84
Step 5:
To calculate the standard deviation, we will use the formula below
[tex]\begin{gathered} \sigma=\sqrt{variance} \\ \sigma=\sqrt{0.84} \\ \sigma=0.917 \end{gathered}[/tex]
Hence,
The standard deviation is = 0.917
