HW 4.1

What is a discrete probability​ distribution? What are the two conditions that determine a probability​ distribution?

A discrete probability distribution lists each possible value a random variable can​ assume, together with its probability.

Decide whether the random variable x is discrete or continuous. x represents the volume of milk taken from one cow for a day.

Continuous

Decide whether the graph represents a discrete random variable or a continuous random variable. Explain your reasoning. Distance a baseball travels after being hit

Continuous, because the variable is uncountable

Number of rainy days in a month

Discrete

Decide whether the graph represents a discrete random variable or a continuous random variable. The home attendance for football games at a university

Discrete​, because home attendance is a random variable that is countable

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. In most​ applications, continuous random variables represent counted​ data, while discrete random variables represent measured data.

False. In most​ applications, discrete random variables represent counted​ data, while continuous random variables represent measured data.

What is the significance of the mean of a probability​ distribution?

It is the expected value of a discrete random variable.

What is a random​ variable?

The outcome of a probability experiment is often a count or a measure. When this​ occurs, the outcome is called a random variable.

What are the two conditions that determine a probability​ distribution? Choose the correct answer below.

The probability of each value of the discrete random variable is between 0 and​ 1, inclusive, and the sum of all the probabilities is 1.

Determine whether the random variable x is discrete or continuous. Explain. Let x represent the distance a baseball travels in the air after being hit.

The random variable is continuous​,because it has an uncountable number of possible outcomes.

Decide whether the random variable x is discrete or continuous. Explain your reasoning. Let x represent the amount of rain (in inches) that fell this spring.

​Continuous, because x is a random variable that cannot be counted.

Decide whether the random variable x is discrete or continuous. Explain your reasoning. Let x represent the time it takes to run a mile.

​Continuous, because x is a random variable that cannot be counted.