APPLIED MATHS STATISTICAL DISTRIBUTIONS

Chapter 6

Random variable

Any variable determined by the outcome of a random event or experiment

Discrete random variable

A random variable which can only take certain values

P(X = x) / p(x) means...

The probability that the outcome of the random variable X is the specific outcome x

Probability distribution

Describes fully the probability of any outcome in the sample space

Ways of displaying the probability distribution of a discrete random variable

1. Probability function

2. Table of probabilities

3. Diagram

Discrete uniform distribution

A discrete probability distribution where all the probabilities are the same

For a discrete random variable, the sum of all the probabilities must add up to...

1

p(x) for a discrete random variable is known as a...

Probability mass function as the probability of each outcome represents an actual 'amount' (i.e. mass) of probability

You can model a random variable X with a binomial distribution B(n, p) if...

1. There are a fixed number of trials, n

2. There are two possible outcomes e.g. success and failure

3. There is a fixed probability of success, p

4. The trials are independent of each other

X ~ B(n, p) means...

X is distributed binomially for n trials with probability p

P(X < a) =

P(X <= a - 1)

P(X > b) =

1 - P(X <= b)

P(X >= c) =

1 - P(X <= c - 1)