book 1

Question 1

How do you write ‘A union B’

Answer 1

P(A∪B)

Question 2

What does (A∪B) mean?

Answer 2

‘A union B’ shorthand for ‘A or B’

Question 3

What does ∅ mean?

Answer 3

∅ represents the empty set

Question 4

What does P(3∪4) mean?

Answer 4

it means the probability P(3 or 4)

Question 5

If it is impossible for A and B to occur simultaneously they are………

Answer 5

mutually exclusive

Question 6

What is P(A ∪ B) = P(A) + P(B) − P(A ∩ B).

Answer 6

The addition rule: for any two events A and B

Question 7

What is the complement ?

Answer 7

is the other outcomes (NOT the ones we want)

Question 8

What does Ω represent?

Answer 8

It is the event space

Question 9

What is the event space?

Answer 9

It is the range - For instance, if the experiment is rolling a six-sided die, then the event space is Ω = {1, 2, 3, 4, 5, 6}

Question 10

What is the range ?

Answer 10

The range is actually comes out of the function, its the set of all possible values a random variable can take

Question 11

What is the domain ?

Answer 11

The domain is what can go into the function

Question 12

What is the codomain ?

Answer 12

The codomain is what may possibly come out of a function

Question 13

What is discrete uniform distribution ?

Answer 13

The random variable X is said to have a discrete uniform distribution, or to be uniformly distributed, if p(x)=1/n, x=1, 2, …..,6. The score obtained when a fair six sided die is rolled can be modelled by a discrete uniform distribution with n=6.

Question 14

What is the Bernoulli distribution ?

Answer 14

A Bernoulli trial is an experiment that has precisely two outcomes: either an event E occurs or it does not. These outcomes are often described as ‘success’ or ‘failure’, and their probabilities are denoted by p and q(=1-p), respectively . A random variable X is said to have a Bernoulli distribution with parameter p if P(X=1)=p and P(X=0)=q. The p.m.f. of X can be written p(x)=p^x q^1-x, x=0, 1.

Question 15

What is the binomial distribution ?

Answer 15

Suppose that a sequence of n independent Bernoulli trials is performed. At each trial either a success occurs, with probability p, or a failure occurs, with
probability 1 − p = q. The total number of successes in n trials is a random variable Y with range {0, 1, . . . , n}.
The random variable Y is said to have a binomial distribution with parameters
n and p, and this is written Y ∼ B(n, p).

Question 16

Independent random variables = P(A ∩ B) = P(A) P(E)

Answer 16

The occurrence of one event does not depend on whether or not the other event has occurred.

Question 17

Mutually exclusive

Answer 17

Heads and tails when tossing a coin is mutually exclusive as you can only get a head or a tail. For playing cards king and hearts can both happen so is not mutually exclusive.

Question 18

Range - discrete

Answer 18

When the range contains a finite or countably infinite number of values it is said to be discrete.

Question 19

Range - continuous

Answer 19

When the range can take any value in an interval of vales is is called continuous.

Question 20

p.m.f - probability mass function

Answer 20

p.m.f of X is px(x) - The probability that X takes on some value x. The p.m.f. of the score on a die is p(x) =1/6 x=1,2,…,6

Question 21

The discrete uniform distribution

Answer 21

Random variable X is said to have a discrete uniform distribution or to be uniformly distributed if p(x)=1/n x=1,2,…..,n. The score obtained when a fair six sided die is rolled can be modelled by a discrete uniform distribution with n=6

Question 22

What is binomial distribution

Answer 22

The binomial distribution is the distribution of the number of successes (x) in a fixed number (n) of independent Bernoulli trials.

Question 23

What is negative binomial distribution

Answer 23

The negative binomial distribution is the distribution of the number of trials needed (x) to get a fixed number of successes (k)