Question

We know that for a probability distribution function to be discrete, it must have two characteristics. One is that the sum of the probabilities is one. What is the other characteristic?

Use the following information to answer the next five exercises: Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events $35\%$of the time, four events $25\%$of the time, three events $20\%$of the time, two events $10\%$of the time, one event $5\%$of the time, and no events 5% of the time.

Short answer

Each random variable $X$has a probability greater than or equal to zero.

Step-by-step solution

Given Information

Sam practices music three times a week. She exercises on a regular basis. $85\%$of the time for all three days, $8\%$of the time for two days, $4\%$of the time for one day, and $3\%$of the time for no days.

Concept Used

A random variable depicts the problem's characteristics and allows us to make decisions. $X$ is the number of days in a week that Ellen has music practice. $P\left(X\right)$is stated to be the probability mass function of a discrete variable $X$ only when, according to the assumptions of discrete distribution,

$\sum P\left(X\right)=1$

Calculation

Another feature of discrete random variables is that they are

$P\left(X\right)\ge 0\text{for all}X$

Conclusion

The feature of a random variable is that it is randomly distributed is

$P\left(X\right)\ge 0\text{for all}X$