Continuous Random Variables
 For continuous random variables we
assign probabilities to intervals not
points.
 Total area under the curve is 1.

P ( a ≤ x ≤ b)
=
area under curve between a and b.
 With continuous variables, each point
has probability zero.
 There is no area over a point.
– P(X = a) = P(X = b) = 0
Normal Distribution
 One type of continuous distribution is
very common, its density function is a
bell-shaped curve.
 This is the density of the normal
distribution.
Shape of the Normal Curve
 The bell is symmetric about the mean of
the random variable.
 The standard deviation of the random
variable affects the spread of the bell.
 The larger the standard deviation is, the
more spread out the bell.
Standard Normal
 The value of µ and σ characterize
which normal distribution we are talking
about.
 The normal distribution with mean = 0
and standard deviation = 1 is called the
standard normal distribution.
Sampling Distribution
The probability distribution of a
statistic over all possible samples
is known as its sampling
distribution.