Stats Exam 4 Conceptual

The factorial formula is

the number of ways to assign every member of a group of size n to n slots

Combination formula

# of ways to choose x objects from a total of n objects where the order in which the x objects are listed does not matter

If two events are mutually exclusive then events A and B both

cannot occur

q is

probability of a failure

Each time a trial is repeated the probabilities of success and failure

remain the same

binomial random variable

the number of successes achieved in the n trials of a Bernoulli process

Mutually exclusive events may share common outcomes of a sample space

False

Permutation formula

# of ways to choose x objects from a total of n objects where the order in which the x objects is listed does matter

The intersection of two events is

A AND B

The union of two events is

A OR B

The complement of event A, within the sample space S is the event consisting of

All outcomes in S that are not in A

A discrete random variable X may assume an infinitely uncountable number of distinct values

False

For two independent events A and B, the probability of their intersection is 0

False

The ounces of soda consumed by an adult next month are an example of a discrete random variable

False

Assume the sample space S = (win, loss). Select the choice that fulfills the requirements of the definition of probability

P (win) = .7, P({loss}) = .3

Cumulative Distribution formula

P(X ≤ x)

What is a characteristic of the mass function of a discrete random variable X

The sum of probabilities P(X=x) over all possible values x is 1 Describes all possible values x with the associated probabilities P(X=x) For every possible value x, the probability P(X=x) is between 0 and 1

Events are collectively exhaustive if

They contain all outcomes of an experiment

A venn diagram represents the sample space for the events

True

Permutations are used when the order in which different objects and arranged matters

True

Risk averse consumer may decline a risky prospect even if it offers a positive expected valye

True

The number of syntactic errors found in a program code would best be described using Poisson probability distribution

True

The relationship between the variance and the standard deviation is such that the standard deviation is the positive square root of the variance

True

Poisson random variable

counts the number of successes over a given interval of time or space

Probability mass function

for a discrete random variable x is a list of the values of X with the associated probabilities, that is, the list of all possible pairs

The complement of event A is the event consisting of all simple events

in the sample space S that are not in A

An analyst has a limit order outstanding on a stock. He argues that the probability that the order will execute before the close of trading is .20. Thus, the odds for the order executing before the close of trading are

one in four

According to the complement rule, the probability of the complement of an event, P(A^c), is equal to

one minus the probability of the event

The expected value is

the long run average value of the random variable over infinitely many independent repetitions of an experiment

It is the poisson process if

the number of successes within a specified time or space interval equals any integer between zero and infinity the numbers of successes counted in non overlapping intervals are independent the probability that success occurs in any interval is the same for all intervals of equal size and is proportional to the size of the interval

Two events are independent if

the occurrence of one event does not affect the probability of the occurrence of the other event

Events are considered dependent if

the occurrence of one is related to the probability of the occurrence of the other