Quantiative Methods - 4.1 - Uniform and Binomial Distributions

Question 1

what does a probability distribution describe? what is worth noting about this?

Answer 1

describes the probabilities of all the possible outcomes for a random variable

• probability of all possible outcomes must sum to 1

Question 2

what is a discrete random variable?

Answer 2

has a finite number of possible outcomes

Question 3

what is a continuous distribution (AKA a continuous random variable)?

Answer 3

has an infinite number of possible outcomes, even if lower and upper bounds exist

Question 4

how is a probability function denoted and what does it specify?

Answer 4

p(x)

- the probability that random variable X takes on the value x

Question 5

what are the 2 key properties of a probability function?

Answer 5

• 0 ≤ p(x) ≤ 1

-  ∑p(x) = 1, the sum of the probabilities for all possible outcomes, x, for a random variable, X, equals 1.

Question 6

what is the difference between discrete and continous distributions?

Answer 6

• discrete distribution, p(x) = 0 when x cannot occur, or p(x) > 0 if it can
• continuous distribution, p(x) = 0 even though x can occur. It is impossible for p(x) to have a value because of the infinite number of possible outcomes

Question 7

what does a cumulative distribution function (cdf) provide? how is it denoted?

Answer 7

the probability that a random variable will be less than or equal to a given value

• F(x) where x is a given value. i.e. the probability the random variable takes on the value x or less

Question 8

what is a discrete uniform distribution?

Answer 8

it has a finite number of possible outcomes, all of which are equally likely

Question 9

what is a continuous uniform distribution?

Answer 9

defined over a range that spans between some lower limit (a) and some upper limit (b) which serve as the parameters of the distribution

• in this case outcomes can only occur between a and b
• since we are dealing with a continuous distribution, even if a < x < b, P(X = x) = 0

Question 10

what is a binomial random variable?

Answer 10

defined as the number of “successes” in a given number of trials, whereby the outcome can be either “success” or “failure”.

the probability of success is constant for each trial and each trial is independent

Question 11

what is a Bernoulli random variable?

Answer 11

a binomial random variable for which the the number of trials is 1