Chapter 4 Test

For a random variable x, the word random indicates that the value of x is determined by chance

True

How to identify Discrete and Continuous Random Vairables

See if the problem states a measurable quantity or a counted quantity. If the quantity can be measured, then it is a continuous random variable. If the quantity can be counted, then it is a discrete random variable.

Random Variable

Assigns a number to each outcome of a random circumstance, or, equivalently, to each unit in a population A discrete random variable would be the number of sales calls a salesperson makes in one day. A continuous random variable would be the hours a salesperson calls in one day

The expected value of a random variable can never be negative

False, it is not equal to the standard deviation of the random variable

The mean of the random variable of a probability distribution describes how the outcomes vary

False. The mean only describes a typical outcome. If it is a constant probability distribution, the variance and standard deviation is zero, otherwise they are positive real numbers

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

The expected value may not be a possible value of x for one trial, but it represents the average value of x over a large number of trials.

unusual probability

a probability of 0.05 or less is considered unusual.

In a binomial experiment with n trials, what does the random variable measure

the random variable can take on values from a finite or countable infintie( e.g, the non-negative integers) set

Discrete probability ddistribution

when the random variable can take only a finite number of countable values. The two conditions that a discrete probability distribution must satisfy is that the probability of each value of the discrete random variable is between 0 and 1, and the sum of all the probabilities is 1.

What does the mean of a probability distribution represent?

It is the expected value of a discrete random variable

Is the expected value of the probability distribution of a random variable always one of the possible values of x?

No, because the expected value may not be a possible value of x for one trial, but it represents the average value of x over a large number of trials

In a binomial experiment, what does it mean to say that each trial is independent of the other trials?

When each trial is independent of the other trials it means that the outcome of one trial does not affect the outcome of the other trials