STA220- Module 6 Discrete Random Variables

What is a random variable?

Variable whose value is a numerical outcome of a random phenomenon

• outcome varies from observation. to observation according to random variable that can be summarized by probabilities

What is a discrete random variable?

A random variable is discrete if the possible outcomes are a set of separate values

• “the number of…” with possible values 0, 1, 2

• ordinal scale of measurement: 1 = strongly disagree.. 3 = neutral… 5 = strongly agree

• continuous if the possible outcomes are infinite continuum, such as all the real numbers between 0 and 1

What is a probability distribution of a random variable?

A probability distribution lists the possible outcomes and their probabilities

• has parameters describing the centre (ex: mean) and the variability (ex: standard deviation)

• assigns a probability to each possible value of the variable (between 0 and 1)

What are parameter values?

The values these measures would assume in the long run, if the randomized experiment of the random sample repeatedly took observations on variable y having the probability distribution

What is the Bernoulli random variable?

Simple random variable with only two outcomes

• success or failure, heads or tails

• y = 1, y = 0

What is the binomial model?

Model that simply counts the number of successes in a series of n independent Bernoulli trials

• makes it easy to find the mean and standar deviation of a Binomial random variable X

What are the properties of the Binomial model?

1. There are a fixed number n observations

2. The n observations are independent

3. Each observation falls into one of just two categories (successes and failure)

4. The probability of a success (call it p) is the same for each observation

How does the shape of a binomial distribution depend on p?

When P < 0.5 = skewed right

P > 0.5 = skewed left

P = 0.5 = symmetric