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Lecture 13

MATH 141 Lecture 13: Statistics 10/27/2016
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Department
MATH - Mathematics
Course Code
MATH 141
Professor
Zhang

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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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Description
Statistics 10272016 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.
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