#### 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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