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# Discrete and Continuous Random Variables

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## Sharon Richards

on 19 June 2014

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#### Transcript of Discrete and Continuous Random Variables

Example: Number of Heads in 4 tosses
Continuous Random Variables
Random variable, X, has an infinite number of values, uncountable.
Takes all values in an interval of numbers.
Use a density curve to show the probability distribution of X, as area under the curve.
The area under a density curve is always 1.
Example: A spinner that generates a random number between 0 and 1.
Discrete Random Variable
Discrete random variable, X, has a countable number of values.
Probability Distribution lists the possible values of X and the probability of each.
Probability of each X must be between 0 and 1.
All P(X) must add up to 1.

Distribution of Continuous Random Variable, x, between 0 and 1
Normal Distributions as Probability Distributions
N(µ, σ)
Standardized variable Z = (X - µ) / σ
Standard normal distribution N(0, 1)
Example: 30% of adults say drugs are most serious problem for schools.
p is the population proportion = .3.
p ˆ is the sample proportion used to estimate p.
Find P(poll differs from true population by more than 2%) if N(.3, .0118).
Discrete and Continuous Random Variables
Section 7.1

Probability Histogram
Probability Histogram for Digits 0-9
Random Variable
A variable whose value is a numerical outcome of a random phenomenon.
Examples:
Number of heads in four tosses of a coin.
Height of 3 year olds.
Number of garages per house in a realtor’s listings.
Amount of milk in one gallon.
Number of televisions in a home.
Number of boys in a family of three children.

Example:
A professor gives 15% A’s and D’s, 30% C’s and B’s, and 10% F’s. Random variable X stands for the student’s grade on a 4 point scale. Write the distribution of X.
Find the P(B or better).
Construct a probability Histogram.
Probability Model of Continuous Random Variables
Assigns probabilities to intervals of outcomes.
Each individual outcome has a probability of 0.
There is no difference between P(X > .8) and P(X ≥ .8).

Practice Density Curve, 7.11
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