Continuous Random Variable

Continuous Random Variable

Take on any value inside an interval (bounded or unbounded)

Probability Density Function

Characterized by the graph of a smooth continuous function f(x) satisfying 1) the total area under the curve f(x) and above the x-axis is equal to 1 and 2) f(x) ≥ 0, for all possible values of x.

RV has a higher chance of taking values near --- than near ---.

x;y

Probability is always represented by…

the area under the curve.

Continuous Uniform Distribution

Defines equal probability over a given range. Rectangular distribution.

Normal Distribution

The most important of all the distributions.

Properties of Normal Distribution

Symmetric about the mean. Different mean and standard deviation corresponds to different distribution.

The smaller the standard deviation…

the narrower the curve.

A change in the standard deviation causes a change in…

the shape of the curve.

A change in the mean causes the graph to…

shift to the right or left.

A positive z score means that…

your x value is greater than the mean.

A negative z score means that…

your x values is less than the mean.

A z score of zero means…

that your x value is equal to the mean.

Standard normal distribution always has…

a fixed mean and standard deviation.