Chapter 8: Probability

Question 1

What is probability

Answer 1

• The measure of trust that an individual places on the occurrence of a future event. When observations cannot be predicted with the certainty called random or stochastic events.
• It is based on long-term relative frequencies

Question 2

What is a sample space

Answer 2

The collection of all possible outcomes of an experiment

Question 3

What is an event

Answer 3

Any subset of the sample space. It is said to have occurred if anyone of its elements is the outcome when the experiment is conducted

Question 4

Experiment

Answer 4

The process of making an observation or taking a measurement that leads to a collection of outcomes

Question 5

What is a random variable

Answer 5

It associates a numerical value with each individual outcome of an experiment

Question 6

Probability of an individual outcome

Answer 6

The probability of an outcome of an experiment can be described as the relative frequency with which the outcome occurs if we repeat the experiment a large number of times

Question 7

Conditions for assigning probabilities to individual outcomes

Answer 7

• The probability of each outcome must be between zero and one
• The probability of all outcomes in the sample space must sum up to 1

Question 8

When is a random variable said to be discrete

Answer 8

If it has either a finite number of values or an infinitely many values that can be grouped in a sequence

Question 9

What is a continuous random variable

Answer 9

It is if a random variable represents some measurement on a continuous scale and is therefore capable of measuring all values in an interval

Question 10

What is the probability density function

Answer 10

It describes the distribution of probability for a continuous random variable

Question 11

What are the properties of a continuous random variable

Answer 11

• The total area under the probability density function/curve is one
• P[a <= X <= b] = area under the probability density curve between a and b
• f(x) >= 0 for all x

Question 12

The most well-known and important continuous distribution is called

Answer 12

It’s called the normal distribution also called the Gauss distribution

Question 13

Properties of a normal distribution

Answer 13

• The parameters mean and standard deviation determine the distribution completely
• The population mean is the position of the centre of the curve
• The population standard deviation determines the maximum height of the curve and the amount of the area in any fixed interval about the mean

Question 14

What is the standard normal probability distribution

Answer 14

The standard normal probability distribution has a bell shaped density with a mean = 0 and a standard deviation = 1

Question 15

What is a parameter

Answer 15

A numerical feature of a population is called a parameter

Question 16

What is a sampling distribution

Answer 16

The probability distribution of a statistic

Question 17

What is the central limit theorem

Answer 17

Whatever the population, the distribution of a sample mean is approximately normal when n is large

Question 18

What is a stochastic event

Answer 18

When observations cannot be predicted with the certainty called random or stochastic events.