Chpt 6 - Continuous Random Variables Flashcards
What is a continuous random variable?
A random variable that cannot be listed, the options are infinite
Generally, I would call them not whole numbers…so how tall are you?
I’m not 5 feet, I’m 5’8” or my weight, even for my personal records isn’t to the whole pound, we use half pounds on nearly all scales
What is a density curve?
A curve showing the distribution of the continuous random variable.
It’s basically created by connecting the tops of the bars of a histogram
What characteristics of a density curve lend itself to a bell-shaped curve?
Unimodal and symmetric
If the distributions of a random continuous variable is unimodal and symmetric, how can we describe the density curve?
Bell-shaped
What shape characteristics are we most concerned about when discussing the shapes of histograms or density curves?
Symmetry, skewness, and modality
What are the 2 parameters that determine a normal distribution?
Mean - a normal curve of a random variable is symmetric about and centered at it’s mean
Standard Deviation - determines the spread of a normal density curve
When looking at a density curve with a μ of 2, where would we expect the peak to be if it is a normal random variable?
2
If a continuous random variable has a bell-shaped density curve, what is the distribution of this random variable called?
Normal distribution
If a continuous random variable has a bell-shaped density curve, what is the random variable called?
Normal random variable
If a continuous random variable has a __________ density curve, the distribution of this random variable is called normal distribution and this random variable is called a normal random variable.
Bell-shaped
How would a normal distribution curve with a σ of 2 compared to another with a σ of 1?
The σ =2 would have
- smaller spread
-values concentrated around μ
-higher peak
How would a normal distribution curve with a σ of 1/2 compared to another with a σ of 1?
The σ = 1/2 would have
- wider spread
-values not concentrated around μ
-flatter peak
What is the notation for a normal random variable?
N(μ, σ)
What is the notation to describe a random variable that has a normal distribution?
X ~ N(μ, σ)
What are the characteristics of the density curve of a standard normal random variable?
μ = 0
σ - 1
A normal random variable with a mean of 0 and standard deviation 1 is called _________. It is denoted as ______. It’s distribution is called a ______.
Standard normal random variable.
Z
Standard normal distribution
If a normal random variable has a mean of 0 and a standard deviation of 1, what is it called?
Standard normal random variable
How is a standard normal random variable denoted?
Z
What is the distribution of a standard normal random variable called?
Standard normal distribution
What is the notation for a standard normal random variable?
Z ~ N (0, 1)