P. STATISTICS LESSON 7 – 1 ( DAY 1 ). DISCRETE AND CONTINUOUS RANDOM VARIABLES. ESSENTIAL QUESTION: What are discrete and continuous random variables, and how are they used to determine probabilities?. To define discrete random variables.
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DISCRETE AND CONTINUOUS RANDOM VARIABLES
Discrete and Continuous are two different ways of assigning probabilities.
A discrete random variable X has a countable number of possible values. The probability of X lists the values and their probabilities:
Values of X: x1 , x2 , x3 , …. Xk
Probability: p1 , p2 , p3 , …pk
The probabilities pi must satisfy two requirements:
Find the probability of any event by adding the probabilities pi of the particular values xi that make up the event.
Two assumptions are made:
When using the table of random digits to select a digit between 0 and 9, the result is a discrete random variable.
The probability model assigns probability 1/10 to each of the 10 possible outcomes.
Continuous random variable is a number at random from 0 to 1.
A continuous random variable X takes all values in an interval of numbers.
The probability distribution of X is described by a density curve.
The probability of any event is the area under the density curve and above the values of X that make up the event.
We assign probabilities directly to events – as areas under a density curve. Any density curve has area exactly 1 underneath it, corresponding to total probability 1.
All continuous probability distributions assign probability of 0 to every individual outcome.
We can see why an outcome exactly to .8 should have probability of 0.
The density curves that are most familiar to us is the normal curves.
Normal distributions are probability distributions. Recall that N(μ, σ) is our shorthand notation for the normal distribution having mean μ and standard deviation σ.
Z = X - μ