Questions: Question 7 1 pt Det x P(x) 0 0.2 1 0.1 2 0.3 3 0.4 Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places.

Solution Steps

The mean \( \mu \) of the probability distribution is calculated as follows:

\[ \mu = 0 \times 0.2 + 1 \times 0.1 + 2 \times 0.3 + 3 \times 0.4 = 1.9 \]

The variance \( \sigma^2 \) is computed using the formula:

\[ \sigma^2 = (0 - 1.9)^2 \times 0.2 + (1 - 1.9)^2 \times 0.1 + (2 - 1.9)^2 \times 0.3 + (3 - 1.9)^2 \times 0.4 = 1.29 \]

The standard deviation \( \sigma \) is the square root of the variance:

\[ \sigma = \sqrt{\sigma^2} = \sqrt{1.29} \approx 1.14 \]

Final Answer