Week 3

Question 1

What is probability?

Answer 1

A number between 0 and 1 that measures that measures the likelihood that some event will occur.
0 means the event is impossible.
1 means the event is certain

Question 2

What is a random experiment?

Answer 2

A process or action that can be repeated under the same conditions but produces different outcomes due to chance.
The specific result of each trial is unpredictable

Question 3

What are basic outcomes?

Answer 3

These are possible outcomes of a random experiment

Question 4

What is sample space?

Answer 4

The set of all possible basic outcomes of a random experiment

Question 5

Example of a sample space?

Answer 5

An investor follows the Dow Jones Index. The sample space is:
- The index is higher than yesterdays close
- The index is not higher than yesterdays close
- The index is equal to yesterdays close

Question 6

What is the rule for sample spaces?

Answer 6

Only one of the possible outcomes can occur. They cannot occur simultaneously

Question 7

What is an event?

Answer 7

An event is a specific set of outcomes from a random event. It is a subset from the sample space, and it can include one or more of the basic outcomes

Question 8

What is intersection of events?

Answer 8

A concept in probability theory, referring to the occurrence of 2 or more events at the same time
The intersection of events represents the event that all the considered events happen together

Question 9

What is a mutually exclusive event?

Answer 9

If events A and B have no common outcomes, they are called mutually exclusive, and their intersection is set to be the empty set, indicating that A and B have no members

Question 10

What is an independent event?

Answer 10

Each event is not affected by other events

Question 11

What is a dependent event?

Answer 11

An event is affected by other events

Question 12

What is Union?

Answer 12

A union refers to the event that at least one of several events occurs.
For 2 events, A and B, the union of A and B, represents the event that either A occurs, B occurs, or both occur.

Question 13

What is meant by an event being collectively exhaustive?

Answer 13

Collectively exhaustive refers to a set of events that covers all possible outcomes of an experiment. In other words, at least one event in the set must occur. Together, these events make up the entire sample space.

Question 14

What are the 2 different types of random variables?

Answer 14

• Discrete
• Continuous

Question 14

What is a random variable?

Answer 14

A numerical value that is assigned to the outcomes of a random experiment.
It maps each basic outcome in the sample space to a number, allowing us to quantify the outcomes of random events

Question 15

What is a discrete random variable?

Answer 15

• Takes on a countable number of distinct values
• E.g the number of heads obtained when flipping a coin 3 times is countable as 0,1,2 or 3

Question 16

What is a continuous random variable?

Answer 16

• Takes on an infinite number of possible values within a given range
• E.g the time it takes for a bus to arrive at a stop, which could be any value within a time interval

Question 17

What is a probability distribution function?

Answer 17

A PDF describes how probabilities are distributed over the values of a random variable. There are two main types of random variables: discrete and continuous, and the nature of the probability distribution depends on the type of variable.

Question 18

What is a discrete probability distribution function referred to as?

Answer 18

• Probability Mass Function (PMF)
• It assigns probabilities to each possible value of the random variable.