Question

Given a probability distribution table: x | p(x) - Complete the table and find the standard deviation.

Answer 1

Main Answer:

To find the standard deviation from a probability distribution table, additional columns for
`\(x \cdot p(x)\) and \((x - \mu)^2 \cdot p(x)\)` need to be computed, where
`\(\mu\)` is the mean. The standard deviation is the square root of the sum of
`\((x - \mu)^2 \cdot p(x)\)`.

Step-by-step explanation:

To calculate the missing values, use the formulae:
`\(x \cdot p(x)\) and \((x - \mu)^2 \cdot p(x)\)`.

After completing the table, find the mean
`\(\mu\) by summing \(x \cdot p(x)\)`. Then, compute
`\((x - \mu)^2 \cdot p(x)\)` for each row. Finally, find the standard deviation by taking the square root of the sum of these values.

The standard deviation measures the spread of the distribution, and this process ensures a comprehensive understanding of the data's variability.

Applying the correct mathematical symbols, such as
`\(\cdot\)` for multiplication, ensures accurate and clear computations.