Answer: [tex]Standard\text{ devaition = 1.29}[/tex]
Explanation:
We have been given the probability distribution table where we have x and the probability of x
To find the standard deviation, we need to know the mean. As a result, we will first find the mean of the distribution
[tex]Mean\text{ = }\sum_{i\mathop{=}1}^nx_iP(x_i)[/tex][tex]\begin{gathered} Mean\text{ = 0 }\times0.3\text{ + 1 }\times\text{ 0.05 + 2 }\times\text{ 0.2 + 2 + 3 }\times0.45 \\ Mean\text{ = 1.8} \end{gathered}[/tex][tex]\begin{gathered} The\text{ formula for standard deviation of a distribution:} \\ Standard\text{ deviation = }\sqrt{\sum_{i\mathop{=}1}^n(x_i-\bar{x}\text{\rparen}^2\text{ }\times P(x_i)} \end{gathered}[/tex]
[tex]\begin{gathered} From\text{ our computation in the table, }\sum_{i\mathop{=}1}^n(x_i-\bar{x})^2\times P(x_i)\text{ = 1.66} \\ Standard\text{ deviation = }\sqrt{\sum_{i\mathop{=}1}^n(x_i-\bar{x}\text{\rparen}^2\text{ }\times P(x_i)} \\ \\ Standard\text{ deviation = }\sqrt{1.66} \end{gathered}[/tex][tex]Standard\text{ devaition = 1.29 \lparen2 decimal place\rparen}[/tex]
