1. **Stating the problem:** We have a random variable $X$ representing the number of customers who order takeout in a day at a café. The values of $X$ are $0, 1, 2, 3,$ and $4$ or more. We need to complete the frequency table, find the mean and variance of $X$, and interpret the results. 2. **Completing the table:** Since the problem does not provide frequencies or probabilities, we assume you have or will provide them. The table should list values of $X$ and their corresponding probabilities $P(X=x)$ such that $$\sum_x P(X=x) = 1.$$ 3. **Mean (Expected value) formula:** $$\mu = E(X) = \sum_x x P(X=x)$$ The mean represents the average number of customers ordering takeout per day. 4. **Variance formula:** $$\sigma^2 = Var(X) = E[(X - \mu)^2] = \sum_x (x - \mu)^2 P(X=x) = \sum_x x^2 P(X=x) - \mu^2$$ Variance measures the spread or variability of the number of customers ordering takeout. 5. **Intermediate work:** - Calculate $\mu$ by multiplying each $x$ by its probability and summing. - Calculate $E(X^2) = \sum_x x^2 P(X=x)$. - Calculate variance as $Var(X) = E(X^2) - \mu^2$. 6. **Interpretation:** - The mean tells us the typical number of takeout customers per day. - The variance tells us how much the daily number of takeout customers fluctuates around the mean. Please provide the probabilities or frequencies to complete the calculations.