To calculate $E[X]$, which represents the expected value (or mean) of the number of takeout orders, we will use the data in the table provided. The expected value $E[X]$ for a sample is the average of the values in the sample.

Here is the data from the table:

• Household 1: 3 takeout orders
• Household 2: 5 takeout orders
• Household 3: 4 takeout orders
• Household 4: 2 takeout orders

To calculate $E[X]$:

$E[X] = \frac{3 + 5 + 4 + 2}{4}$

Let me compute that for you.The expected value $E[X]$ of the number of takeout orders is $3.5$.

Would you like further explanation or have any additional questions?

Here are 5 related questions to expand on this:

1. How would you calculate the variance of this sample data?
2. What is the significance of $E[X]$ in probability theory?
3. How does the sample mean $\bar{X}$ compare to the population mean?
4. Can you estimate the median number of takeout orders from this data?
5. What other measures of central tendency could you use here?

Tip: When calculating $E[X]$ for a sample, ensure that all values are from a representative sample to minimize bias.