STA013 - Fall 24 Quiz 5

Events A and B are said to be independent if and only if the probability of event B is not influenced or changed by the occurrence of event A, or vice versa

Events A and B are said to be independent if and only if the probability of event B is not influenced or changed by the occurrence of event A, or vice versa

Independent Events

The probability of an event A, given that event B happened is the ________________ and is written as P(A | B)

conditional probability

Mutually exclusive events are ____ independent

not

__________ is the event the test is positive for a given condition, given that the person does not have the condition

false positive (type I error)

________________ is the event that the test is negative for a given condition, given that the person has the condition

false negative (type II error)

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

random variable

Quantitative random variables are classified as either ________ or ________, according to the values that X can assume

discrete, continuous

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

relative frequency

Now we define probability distribution for a random variable X as the __________________ constructed for the entire population of measurements

relative frequency 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

probability distribution

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 ___

1

The difference between a probability distribution and a relative frequency distribution is that the relative frequency distribution describes a _________ of n measurements, while the probability distribution is constructed as a model for the _______________ of measurements

sample, entire population

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

E, on average

The mean or ______________ of X is given as μ = E(X) = Σx p(x) summing over all the values of X

expected value

Let X be a discrete random variable with probability distribution p(.) and mean μ. The _________ of X is σ^2=E(x-μ)^2=∑(x-μ)^2p(x)

variance

The standard deviation σ of a random variable X is equal to the __________________ of its variance

positive square root

One characteristic of a binomial experiment is that the experiment consists of n ___________ trials

identical

One characteristic of a binomial experiment is that each trial results in one of ____ outcomes. One outcome is called a success, S. The other is a failure, F

two

One characteristic of a binomial experiment is that 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

p, 1-p

One characteristic of a binomial experiment is that the trials are ____________

independent

One characteristic of a binomial experiment is that we are interested in the ________ random variable X, the number of successes in n trials, for X =___________

discrete, 0,1,2....n