What is true about the cumulative distribution function (cdf) of a discrete random variable?Group of answer choicesIt is step-wise increasing and eventually approaching 1.It may take negative value; for example when the random variable of interest is temperature.Its value can decrease, but eventually it must approach 1.It is not related to the probability distribution function (pdf) of the random variable at all, because it measures different quantities compared to pdf.

The correct answer is: "It is step-wise increasing and eventually approaching 1."

Here's why:

1. The cumulative distribution function (CDF) of a discrete random variable is a step-wise function. This is because the CDF at a given value x is defined as the probability that the random variable takes a value less than or equal to x. For a discrete random variable, this probability increases in steps as x increases.

2. The CDF of a random variable, whether discrete or continuous, always lies between 0 and 1 (inclusive). Therefore, it cannot take negative values.

3. The CDF of a random variable cannot decrease. This is because as we increase the value of x, we are considering a larger set of outcomes for the random variable, so the probability (i.e., the value of the CDF) can only stay the same or increase.

4. The CDF of a random variable is related to its probability distribution function (PDF). For a discrete random variable, the CDF at a given value x is the sum of the PDF at all values less than or equal to x. So, the CDF and PDF measure related quantities.