Reading and Validating Discrete Probability Distributions

All flashcards

What is a discrete probability distribution?

It is a list of the possible values of a discrete random variable paired with the probability of each value.

What does $P(X=x)$ mean?

It is the probability that the random variable $X$ takes the particular value $x$.

What are the two conditions for a valid discrete probability distribution?

Every probability must be between zero and one, inclusive, and the probabilities for all possible values must sum to one.

Why must the probabilities in a distribution sum to one?

The listed values cover the possible outcomes, so one of them must occur. Their combined probability is therefore 1.

How is a sample-based probability such as $\frac{23}{50}$ interpreted?

It means that 23 of the 50 observations had the outcome represented by that value of the random variable.

Quiz questions

1. What does a random variable do in a chance process?Answer: It assigns a numerical value to each outcome.
2. If $P(X=x)=0.3$, what does this notation state?Answer: The probability that $X$ equals $x$ is 0.3.
3. In a sample of 50 mothers, 23 report two newborn wake-ups per week. What sample-based probability corresponds to two wake-ups?Answer: $\frac{23}{50}$
4. Nancy attends classes three days a week 80% of the time, two days 15% of the time, one day 4% of the time, and no days 1% of the time. What is the probability that she attends all three days?Answer: $0.80$
5. A baker assigns probabilities $0.15$, $0.35$, $0.40$, and $0.10$ to making 1, 2, 3, and 4 batches, respectively. Which number of batches has the greatest probability?Answer: 3 batches