6.1 Probability distributons

Question 1

What is a random variable?

Answer 1

» A variable whose value depends on the outcome of a random event

Question 2

What is the sample space?

Answer 2

» The range of values that a random variable can take

Question 3

When is the variable discrete?

Answer 3

» If it can only take certain numerical values

Question 4

When is the variable random?

Answer 4

» If the outcome is not known until the experiment is carried out

Question 5

How are random variables written?

Answer 5

» Using upper case letters

Question 6

How are the particular values using the random variable written?

Answer 6

» Using equivalent lower case letters

Question 7

What is the probability that the random variable X takes a particular value x?

Answer 7

» P(X = x)

Question 8

What does P(X = x) show?

Answer 8

» P is the probability that…
» X is the outcome of the random variable X
» x was the specific ouutcome

Question 9

What does a random variable represent?

Answer 9

» A single experiment/trial

Question 10

What is the shorthand for P(X = x)?

Answer 10

» p(x)

Question 11

What does the probability distribution fully describe?

Answer 11

» The probability of any outcome in the sample space

Question 12

Describe how the probability mass function of a dice would look like?

Answer 12

» First row would be x : 1 , 2 ,3 ,4 ,5 ,6
» P(X = x) Would equal 1/6 for all of them

Question 13

What is uniform distribution?

Answer 13

» When all the probabilities are the same

Question 14

What are the 2 ways to write the mapping from outcomes to probabilities?

Answer 14

» As a function
» As a table

Question 15

How do you write the probability mass as a function?

Answer 15

» p(x) = piecewise bracket(0.1x, x = 1,2,3
(O, otherwise)

Question 16

What are the advantages of writing the mapping as a function?

Answer 16

» Can have a rule expression base on the outcome

Question 17

What are the advantages of writing the mapping as a table?

Answer 17

» Explicit

Question 18

What is the equation to caclulate the sum of the probabilities of all outcomes of an event which add up to one?

Answer 18

» For a random variable X
» ΣP(X = x) = 1