Probability

Question 1

What is an inferential process?

Answer 1

Collection of techniques that allows us to draw conclusions at N level from a sample (n)

Question 2

Can we drawn N from a non-probability sampling when doing an inferential process?

Answer 2

No, because a non-probability sampling isn’t prevented from biases and have an over/under-representation of given groups.

Question 3

What is a support?

Answer 3

The set of all possible values taken by a random variable

Question 4

What are the two types of numerical values a random variable can take?

Answer 4

Discrete = finite or infinite set of values that are COUNTABLE
Continues = infinite non countable sets with values that can be between any two numbers

Question 5

What is the probabilistic function for discrete variables?

Answer 5

Pi=Pr(X=xi)

Question 6

What are the properties of the probabilistic function for discrete variables?

Answer 6

0 <= pi<= 1 for i =1,2,…,k (represents a probability, thus it has to be greater than 0 and less than 1, because:)
p1+p2+….+pk=1 (the sum of all probabilities is 100%, 1)

Question 7

What is the graph used to represent discrete random variables?

Answer 7

Bar chart

Question 8

What does the Expected value represents?

Answer 8

The theoretical mean, that is, the center of the distribution value at which we have a balancing of probabilities
Denoted by μ

Question 9

How can we calculate the expected value (μ) for discrete random variables?

Answer 9

The sum of the multiplication of each value of X by its chance of occurring.
(Like for weighted samples, but instead of multiplying by the weight, we do it by the probabilities)

Question 10

What does the variation and the standard deviation represent?

Answer 10

The spread of the values around the expected value (the mean, μ)

Question 11

How can we calculate the variance for discrete random variables?

Answer 11

σ2= Σ(X-μ)^2*p(x)

Question 12

How can we calculate the standard variation?

Answer 12

Square root of σ2 (variance)

Question 13

Can we calculate quartiles and the median for discrete rand. variables?

Answer 13

Yes

Question 14

In which type of events do we have a Bernoulli distribution?

Answer 14

• 1 trial
  -2 possible outcomes
  Notation: X~Bern(p)

Question 15

What is the Variance formula for a Bernoulli distribution?

Answer 15

σ2= p (1-p)

Question 16

What is the Expected value for a Bernoulli distribution?

Answer 16

E(X) = p

Question 17

When do we have a Binomial distribution?

Answer 17

-n times
-2 possible trials
Notation: X~Bin(n,p)

Question 18

What is the Binomial coefficient?

Answer 18

n!/x!(n-x)!

Question 19

What is the Binomial distribution formula?

Answer 19

[n!/x!(n-x)!] * p^x(1-p)^(n-x)

Question 20

What is the Expected value for a Binomial distribution?

Answer 20

μ=np

Question 21

What is the Variance formula for a Binomial distribution?

Answer 21

σ2= np (1-p)

Question 22

For a continuous variable, can we have a probability =a?

Answer 22

No, it would be 0. Probabilities for continuous variables are ONLY for INTERVALS

Question 23

What are the properties of the probabilistic function for continous variables?

Answer 23

f(x) >= 0 for all x

The area under the entire curve = 1

Question 24

How do we represent a continuous probabilistic function?

Answer 24

Density function

Question 25

Which one is a linear operator: variance or Expected value?

Answer 25

Expected value, the variance stays the same if we add a constant to the variable

Question 26

What is the formula for standardization?

Answer 26

Z= (X-μ)/σ

Question 27

What is the mean of an standardized variable?

Answer 27

Zero

Question 28

What is the formula for Expected Value and Variance in linear transformation?

Answer 28

E(x)=a+bμ

Var(x) = b^2(σ^2)

Question 29

What is the model for linear transformation?

Answer 29

Y=a+bX

Question 30

What is the variance of an standardized variable?

Answer 30

1

Question 31

How is normal distribution denoted?

Answer 31

X~n(μ,σ2)

Question 32

For a given mean increasing the variance would produce what type of curve?

Answer 32

Flatter and wider curve

Question 33

For a given mean decreasing the variance would produce what type of curve?

Answer 33

Taller and narrower curve

Question 34

What are the characteristics for a standard normal distribution?

Answer 34

μ= 0
σ2 = 1

Question 35

How is standard normal distribution denoted?

Answer 35

X~n(0,1)