01 Probability

Question 1

random variable

Answer 1

a random variable attaches a value to each possible outcome of a random process

Question 2

outcomes

Answer 2

outcomes are the mutually exclusive results of the random process and the set of all potential outcomes is called the sample space

Question 3

probability distribution

Answer 3

The (marginal) probability distribution is the set of all possible outcomes and their associated probabilities

Question 4

cumulative probability distribution

Answer 4

The cumulative probability distribution is the probability that the random variable is less than or equal to a particular value

Question 5

joint distribution

Answer 5

The joint distribution is the probability that two (or more) random variables take on certain values simultaneously

Question 6

conditional distribution

Answer 6

Conditiona distribution is the distribution of a random variable Y conditional on another random variable X taking on a specific value.

P(Y = y | X = x) = P(X = x, Y = y) / P(X = x)

Question 7

relevant distributions

Answer 7

normal distribution
chi-square distribution
student t distribution
F distribution
Bernoulli distribution

Question 8

expectations

Answer 8

E(X) = sum(xi fx(xi))
Var(X) = E(X^2) - E(X)^2

Question 9

E(aX)

Answer 9

aE(X)

Question 10

E(X + Y)

Answer 10

E(X) + E(Y)

Question 11

Var(aX)

Answer 11

a^2 Var(X) = b^2 σ^2

Question 12

Var(aX + bY)

Answer 12

a^2 σ(x)^2 + 2 ab σ(xy) + b^2 σ(y)^2

Question 13

random sampling

Answer 13

selected at random and i.i.d

Question 14

i.i.d

Answer 14

independently and identically distributed:

• Same marginal distribution
• The value of Y1 provides no information about the value of Y2

Question 15

law of large numbers

Answer 15

Under general conditions, the sample average will be close to the population mean with very high probability when the sample is large

Question 16

CLT

Answer 16

central limit theorem

Question 17

central limit theorem

Answer 17

Under general conditions, the sampling distribution of the standardized sample average is well approximated by a standard normal distribution when the sample size is large