Question

Suppose that you make a large number of independent observations of a random variable and then construct a table giving the possible values of the random variable and the proportion of times each value occurs. What will this table resemble?

Short answer

The potential values of the random variable, as well as the proportion of times each value happens, are listed in a table. The table is a representation of the probability of the random variable X.

Step-by-step solution

Step 1. Given information

"Assume you collect a large number of independent observations of a random variable and then create a table containing the random variable's potential values and the fraction of times each value occurs. "

Step 2. Solution

The potential values of the random variable, as well as the proportion of times each value happens, are listed in a table. The table mimics the random variable's probability. Consider the case of a random variable X, which can take one of two values: 1 or 2. The variable X is as follows in a total of 100 experiments:

Random Variable (X)	Number of times
1	40
2	60

Here, By $\frac{f}{N}$ rule:

$$\begin{gathered} P(X=1)=40 \\ =0.4 \\ P(X=2)=60 \\ =0.6 \end{gathered}$$