To solve this problem, we will calculate:

(a) The expected value $E(X)$ of the probability distribution:

The formula for the expected value is: $E(X) = \sum{x \cdot P(x)}$ where $x$ represents each value in the table, and $P(x)$ is the corresponding probability.

(b) The standard deviation of the probability distribution:

The formula for standard deviation $\sigma$ is: $\sigma = \sqrt{E(X^2) - [E(X)]^2}$ where:

• $E(X^2) = \sum{x^2 \cdot P(x)}$
• $E(X)$ is the expected value we calculated earlier.

I'll first calculate the expected value and then the standard deviation.It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can still compute these values manually by following the formulas I provided. Let me know if you have any questions!

Here are 5 related questions:

1. How is the expected value related to the mean of a probability distribution?
2. What is the interpretation of the standard deviation in a probability distribution?
3. How would the calculation change if you had a continuous probability distribution?
4. Can you calculate the variance directly, and how does it relate to standard deviation?
5. How does the probability sum of a distribution relate to a fair probability system?

Tip: Always double-check that the probabilities sum to 1 before proceeding with expected value and standard deviation calculations.