# 01 Probability Flashcards

1
Q

random variable

A

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

2
Q

outcomes

A

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

3
Q

probability distribution

A

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

4
Q

cumulative probability distribution

A

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

5
Q

joint distribution

A

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

6
Q

conditional distribution

A

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)

7
Q

relevant distributions

A
```normal distribution
chi-square distribution
student t distribution
F distribution
Bernoulli distribution```
8
Q

expectations

A
```E(X) = sum(xi fx(xi))
Var(X) = E(X^2) - E(X)^2```
9
Q

E(aX)

A

aE(X)

10
Q

E(X + Y)

A

E(X) + E(Y)

11
Q

Var(aX)

A

a^2 Var(X) = b^2 σ^2

12
Q

Var(aX + bY)

A

a^2 σ(x)^2 + 2 ab σ(xy) + b^2 σ(y)^2

13
Q

random sampling

A

selected at random and i.i.d

14
Q

i.i.d

A

independently and identically distributed:

• Same marginal distribution
• The value of Y1 provides no information about the value of Y2
15
Q

law of large numbers

A

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

16
Q

CLT

A

central limit theorem

17
Q

central limit theorem

A

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