Question

instructions. show all your work to get full credit. circle your final answers. exam is worth 40 points that is 20% of your final grade.

1. (4 points) given the following probability distribution:

(a) find the mean μ.
(b) find the standard deviation σ.

Explanation:

Step1: Calculate the mean $\mu$

The formula for the mean of a discrete probability distribution is $\mu=\sum_{i}x_{i}f(x_{i})$.

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Step2: Calculate the variance $\sigma^{2}$

The formula for the variance is $\sigma^{2}=\sum_{i}(x_{i}-\mu)^{2}f(x_{i})$.

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Step3: Calculate the standard deviation $\sigma$

Since $\sigma=\sqrt{\sigma^{2}}$, and $\sigma^{2} = 4$, then $\sigma=\sqrt{4}=2$.

Answer:

(a) The mean $\mu$ is $6$.
(b) The standard deviation $\sigma$ is $2$.