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Statistics

10/27/2016

Continuous random variable

A random variable assumes values within intervals, i.e. all values inside the interval can be

assumed.

Most commonly used measurements can be recognized as continuous random variable, such as

1. Weight

2. Height

3. Area

4. Time

Notation

Again, use capital letters, such as X, Y, Z, to name a random variable

we can express the possible values of the random variable as following:

or

Examples

1. Age of college students: X in [18, 30]

2. Temperature of a classroom: T in [60 Degrees, 90 Degrees]

Function, Equation and variable

In calculus, we know a function or equation can describe the relationship between outcomes

and values of variable.

The value of variable is all possible candidates for your random variable; and the outcome is

the probability of each candidate.

Density function

A density function is a formula to describe the chance of each possible choice of a continuous

random variable in the intervals

Notation: f(x), g(x), etc.

Properties

1. f(x) 0

2. The total area between the curve f(x) and x-axis is 1.

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