Stats1- Probability and Random Variables

Question 1

What is probability

Answer 1

measure of how likely it is for an event to happen

Question 1

Random Experiment is an experiment characterized by…

Answer 1

an uncertain outcome.

Question 2

• Sample space Ω.
• P(Ω)
• What is an event in relation to the sample space Ω?
• P(Event) what is it? Value between…complement of p(event) what is it?

Answer 2

• the set of all possible outcomes of the experiment.
• 1
• an event is a subset of the sample space
• probability that an event occurs, it is a value between 0 and 1.
• The complement of p(event) is the probability that the event does not occur.

Question 3

• What does it mean that 2 events are mutually exclusive (disjoint events)?

If 2 events are mutually exclusive what is:
- probability of the union;
- conditional probability;
- joint probability.

Answer 3

• 2 events are disjoint (mutually exclusive) if the occurrence of one implies the non occurrence of the other.
• probability of the union is P(A)+P(B).
• conditional probability P(A |B)= 0.
• joint probability P(AnB) = 0.

Question 4

What does it mean that 2 events are joint events?
What is the probability of the union?

Answer 4

It means that they are not mutually exclusive and so the occurrence of one event does not exclude the occurence of the other event.

The probability of the union is P(AuB) = P(A)+P(B)-P(AnB)

Question 5

When can 2 events be considered independent events?
- What is the joint probability of 2 independent events?

Answer 5

Independent events if the occurrence of one event does not affect the occurrence of the other.

P(AnB) = P(A)*P(B).

Question 6

What does it mean “conditional probability”?
How is it calculated?

Answer 6

It is the probability of event A given the occurence of event B.

P(A |B) = P(AnB) / P(B)

Question 7

What is the expected value?

Answer 7

Given an experiment with
- possible outcomes a1, a2…an;
- which occur with probabilities p1, p2…pn.

The expected value is the summation of ai * pi for each i that goes from 1 to n.

Question 8

What is a permutation?

What is a r-permutation?
How do you calculate P(n, r)?

Answer 8

A permutation of a set of objects is an ordering of the objects in a row.

An r-permutation of a set of n-elements is an ordered selection of r elements taken from a set with n elements.

P(n,r)= n! / (n-r)!

Question 9

What is a r-combination?
How do you calculate Cn,r?

Answer 9

Is the number of subsets of size r that can be chosen from a set of n elements.

Cn,r = n! / r!(n-r)! = (n r)