Lecture 5 Quiz Material

independent, dependent events

There is a rule that can be used to calculate the probability of the intersection of several events. This rule depends on the concept of _______ or _______.

independent

Two events, A and B, are said to be _______ if and only if the probability of event B is NOT influenced or changed by the occurrence of event A, or vice versa.

conditional probability of A, given that B has occurred

The probability of an event A, given that the event B has occurred, is called _______, _______ ,and written as P(A/B).

independent

When two events are _______ that is, if the probability of event B is the same, whether or not event A has occurred, then event A does not affect vent B and P(B/A) = P(B).

and, and

Since colorblind people can be either male or female, the event A, which is that a person is colorblind, consists of both those simple events that are in A _______ B and those simple events that are in A _______ B^c.

mutually exclusive and exhaustive

Suppose now that the sample space can be partitioned into k subpopulations, S1, S2, S3, ... Sk, that, as in the colorblindness example, are _______; that is, taken together they make up the entire sample space.

Law of Total Probability

You can go one step further and use the Multiplication Rule to write P(A n Si) which the result is known as the _______.

false positive (type I error)

A _______ is the event that the test is positive for a given condition, given that the person does not have the condition.

false negative (type II error)

A _______ is the event that the test is negative fora given condition, given that the person has the condition.

random variable

A variable X is a _______ if the value that it assumes, corresponding to the outcome of an experiment, is a chance or random event.

binomial distribution

A special discrete probability distribution is _______.

discrete, continuous

As in earlier chapter, quantitative random variables are classified as either _______ or _______ , according to the values that X can assume.

relative frequency

We defined probability as the limiting value of the _______ as the experiment is repeated over and over again.

probability distribution, relative frequency distribution

Now we define the _______ for a random variable X as the _______ constructed for the entire population of measurements.

probability distribution

The _______ for a discrete random variable is a formula, table, or graph that gives all the possible values of X, and the probability p(x) = P(X=x) associated with each value x.

1

The values of X are mutually exclusive events; summing p(.) over all values of X is the same as adding the probabilities of all simple events and therefore equals _______.

sample, entire population

The difference is that the relative frequency distribution describes a _______ of n measurements, while the probability distribution is constructed as a model for the _______ of measurements.

E(X), on average

The population mean, which measures the average value of X in the population, is also called the expected value of the random variable X and is written as _______ (sometimes 𝜇). It is the value that you would expect to observe _______ if the experiment is repeated over and over again.

expected value

Let X be a discrete random variable with probability distribution p(.). The mean or of X is given as μ = E(X) = Σx p(x).

variance

Let X be a discrete random variable with probability distribution p(.) and mean μ. The variance of X is summing over all the values of X.

standard deviation σ of a random variable X, positive square root

The _______ is equal to the _______ root of its variance.

binomial experiment

A _______ is one that has these five characteristics.

identical

The experiment consists of n _______ trials

two

Each trial results in one of _______ outcomes. For lack of a better name, one outcome is called a success, S, and the other a failure, F

p, (1-p)

The probability of success on a single trial is equal to _______ and remains the same from trial to trial. The probability of failure is equal to _______= q.

independent

The trials are _______.

discrete random variable X, 0-n

We are interested in the _______, the number of successes in n trials, for X = _______.