Lecture 3 Flashcards
Random variable
A random variable is a variable that associates a numerical value with each possible outcome of an experiment
two types of random variables
Continuous and discrete
Continuous random variable
Continuous random variables can assume any values contained in one or more intervals (i.e. infinite and uncountable)
Discrete random variables
Discrete random variables can assume a countable number of values, finite or infinite
Discrete probability distribution
The probability distribution of a discrete random variable is a graph, table, or formula that specifies the probability associated with each possible value the random variable can assume
discrete unifrom probability distribution (formula)
If all possible values that the variable can assume are equally as likely then the discrete probability distribution is defined as
P(X=x) = p(x) = 1/n
Uppercase and lowercase letters
Upper - random variables
Lower - realized values
Discrete probabilities - at most and at least a certain number (formula)
Most: P(X < or equal x)
Least: P(X > or equal x)
Is it possible to calculate the populations expected value?
Yes, if the probability distribution is known
Is it possible to calculate the population variance and standard deviation?
Yes, if the probability distribution is known
The Bernoulli distribution (values)
May only take on the values 0 and 1
The binomial distribution
The binomial distribution is a sequence of identical Bernoulli trails with probability: in other words “number of successes in a sample of n observations”
characteristics of a binomial experiment
- the experiment consists of n identical bernoulli trials
- there are only two possible outcomes in each trial
- the probability of 1 is denoted by pi
- the probability of 0 is denoted by 1-pi
- the trials are independent
