STA 13 Midterm 2

What is uniform distibution?

Simplest distribution. Continuous distribution that has constant probability. It gives equal probability to all interval

X ~ Uniform(a,b)

• a = min

• b = max

Curve = prob. density function

All probabilities are positive

Function for Uniform Distribution

What distribution does NOT care about equality sign?

Uniform Distribution

How do you turn variance into the standard deviation?

Square root the variance

If selecting samples of size n ≤ 30 from a population with a known mean and standard deviation, what requirement, if any, must be satisfied in order to assume that the distribution of the sum is a normal distribution?

The population must have a normal distribution.

What is the central limit theory?

What does x̄ represent

What does X̄ represent

A random variable that represents the mean of all possible sample means

What does Σx mean

What does P(x) mean

The probability that X takes on the value of x. P(x=0) or P(x=1)

What is a random variable

They are typically denoted with capital letters (X,Y, Z). A random variable is a function that assigns a numerical value to each outcome in the sample space

Which ways can a probability distribution be listed

Tables, functions, or graphs

What are the two characteristics of a discrete probability distribution

1. Each probability is between 0 and 1, inclusive. 0 ≤ p(x) ≤ 1

2. The sum of the probabilities is 1

Is a table

What is the expected value

The “long-term” average or mean. If you conduct the experiment over and over, you would expect this average

What is a binomial distribution

Probability distribution that models the probability obtaining to TWO outcomes (“success” or “failure”), a certain number of times (x), out of a fixed number of trials (n), of a discrete random event.

How do you calculate the expected value in Binomial Distribution

Expected = (n)(p)