Given the probability distribution of the number of successes when treating four patients with a specific medicine:

Successes (X)	Probability P(X)
0	0.24
1	0.08
2	0.14
3	0.31
4	0.23

Here are some useful calculations:

1. Expected Value (Mean, $E(X)$):

$E(X) = \sum X \cdot P(X)$

2. Variance ($Var(X)$):

$Var(X) = E(X^2) - [E(X)]^2$ where $E(X^2) = \sum X^2 \cdot P(X)$

3. Standard Deviation ($\sigma$):

$\sigma = \sqrt{Var(X)}$

Would you like me to compute these values? Let me know if you have any questions!

Related Questions:

1. How do you interpret the expected value in this context?
2. What does variance tell us about the data?
3. How can we check if this is a binomial distribution?
4. How do you find cumulative probabilities from this distribution?
5. How can we use this distribution to predict outcomes for larger groups?

Tip:

The expected value represents the average number of successes if the experiment were repeated many times.