Year 1 Chapter 6: Statistical Distributions

Question 1

What is a probability distribution?

Answer 1

The probability of any outcome in a sample space.

Question 2

What do the sum of probabilities of all outcomes of an event add up to?

Answer 2

1.

Question 3

When can you model X with a binomial distribution?

Answer 3

If there are a fixed number of trials “n”.

If there are two possible outcomes (success or failure).

If there is a fixed probability of success “p”

If the trials are independent of each other.

Question 4

What is the probability mass function given by if a random variable X has a binomial distribution?

Answer 4

P(X = r) = (nCr)(p^r)(1 - p)^(n - r)

Question 5

How would you calculate the probability that X is greater than 5?

Answer 5

X > 5
= 1 - P(X ≤ 5)

Question 6

How would you calculate the probability that X is no more than 3?

Answer 6

X ≤ P(X ≤ 3)

Question 7

How would you calculate the probability that X is at least 7?

Answer 7

X ≥ 7
= 1 - P(X ≤ 6)

Question 8

How would you calculate the probability that X is at most 8?

Answer 8

X ≤ 8
= P(X ≤ 8)

Question 9

How would you calculate the probability that X is fewer than 10?

Answer 9

X < 10
= P(X ≤ 9)

Question 10

What is an easy way to remember <, >, ≤, ≥ conversions?

Answer 10

When X > x, 1 - P(X ≤ x)

When X ≥ x, 1 - P(X ≤ x-1)

When X < x, P(X ≤ x-1)

Question 11

How do you represent a probability mass function?

Answer 11

. . . . . . . . . { 1/8 . . . . x = 0, 3
P(X = x) = { 3/8 . . . . x = 1, 2
. . . . . . . . . { 0 . . . . . .otherwise