Probability Distribution

Question 1

How is a random variable represented?

Answer 1

By a capital letter, e.g, (X, Y, Z) that takes on values that are outcomes of an experiment

Question 2

What does a lower case letter mean?

Answer 2

It represents the value the upper case letter takes
E.g, P(X=x)

Question 3

What are the ways that probability distribution can be represented as?

Answer 3

1. Table form
2. Mass function form

Question 4

Write the mass function form for a number that a fair 6 sided dice lands on

Answer 4

P(X=x) = { ⅙ if x= 1,2,3,4,5,6

Question 5

What’s a discrete random variable?

Answer 5

A variable that takes finite number of values

Question 6

What’s a continuous variable

Answer 6

It takes on infinite number of values

Question 7

When are events independent

Answer 7

When P(A and B)= P(A) x P(B)

Question 8

When does binomial distribution take place? (BINS)

Answer 8

B- binary (two possible outcomes eg. Success or failure)
I- independent (trials must be independent)
N- Number of trials
S- success (the probability of success)

Question 9

How is the binomial distribution written?

Answer 9

X ~ B ( n, p )

N= number of trials
P= probability

Question 10

When is binomial PD and CD used?

Answer 10

Binomial PD is used when ‘ = ‘
Binomial CD is used when less than or equal

Question 11

How would you work out P(X < r)?

Answer 11

P( X ≤ r- 1)
E.g: P(X < 6) = P(X ≤ 5)

Question 12

How would you work out P (X > r)?

Answer 12

1 - P( X ≤ r)
E.g: P(X > 5) = 1 - P( X ≤ 5)

Question 13

How would you work out P(X ≥ r)?

Answer 13

1 - P( X ≤ r -1)
E.g: P(X ≥ 7) = P(X ≤ 6)