The Solution:
Given:
Required:
Find the standard deviation of the probability distribution.
Step 1:
Find the expected value of the probability distribution.
[tex]E(x)=\mu=\sum_{i\mathop{=}0}^3x_iP_(x_i)[/tex][tex]\begin{gathered} \mu=(0\times0.25)+(1\times0.05)+(2\times0.15)+(3\times0.55) \\ \\ \mu=0+0.05+0.30+1.65=2.0 \end{gathered}[/tex]
Step 2:
Find the standard deviation.
[tex]Standard\text{ Deviation}=\sqrt{\sum_{i\mathop{=}0}^3(x_i-\mu)^2P_(x_i)}[/tex][tex]=(0-2)^2(0.25)+(1-2)^2(0.05)+(2-2)^2(0.15)+(3-2)^2(0.55)[/tex][tex]=4(0.25)+1(0.05)+0(0.15)+1(0.55)[/tex][tex]=1+0.05+0+0.55=1.60[/tex]
Thus, the standard deviation is 1.60
Answer:
1.60
