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HW- pgs. 475-476 (7.8-7.10)
7.1 Quiz THURSDAY
Ch. 7 Test THURSDAY 12-22
www.westex.org HS, Teacher Website
12-13(=)-11
Warm up—AP Stats
Welcome back to class James. To reacclimate you
to AP Stats class I am giving you a chance to pick a
number between 0 and 1. I will have a random
number generator pick a number. What is the
probability that James will pick the same number?
Are you reacclimated James?
Name _________________________
AP Stats
7 Random Variables
7.1 Day 2 Discrete & Continuous Random Variables
Date _______
Objectives
 Define a density curve.
 Explain what is meant by a uniform distribution.
 Define a continuous random variable and a probability distribution for a continuous
random variable.
Continuous Random Variables
When we use a table of __________ digits to select a digit between 0 and 9, the result is a
1
discrete random variable. The probability model assigns probability
to each of the 10
10
possible outcomes.
What if we wanted to choose a number at random between 0 and 1? To visualize this think of a
spinner marked from 0 to 1. The sample space is now an entire ____________ of numbers:
S = {all numbers x such that 0  X  1 }
Can we assign the probability of getting a .238? How about the probability of getting between
a .3 and a .4?
We can’t add up individual value’s probabilities as we did with discrete random variables. Why?
***
***
With continuous random variables the way to assign probabilities to events is by finding the
_______ under a density curve, such as a normal curve or simple functions which we can use
geometry to compute the areas. Any density curve has an area exactly _____ underneath it,
corresponding to a total probability of 1. Take a look at example 7.3…
The probability distribution of a continuous random variable assigns probabilities as area under
a density curve. See figure 7.6.
***A continuous random variable X takes all values in an ____________ of numbers. The
probability of any event is the _______ under the density curve and above the values of that
make up the event*** See figure 7.6 above.
REMEMBER---Every individual outcome has a probability of _____ for continuous probability
distributions‼! You need an INTERVAL to assign positive probabilities. Since the probability of
X = 0.7 is), it should make sense that the events X ≥ 0.7 and X > 0.7 have the same probability.
With continuous random variables (but not ___________) it doesn’t make sense to make a
distinction between ≥ and > when finding probabilities.
***Again, think of probabilities in continuous random variables as areas under a density curve.
What is the area under a density curve above 0.7? What’s the width of 0.7? IT HAS NO
WIDTH‼!! We need an interval in order to have a width so that we can find the AREA above
the interval and below the density curve. Since there can’t be an area above a single point, such
an even would have a probability of _____.***
Normal Distributions as Probability Distributions
Normal curves are one example of density curves. (from section 2.2) Density curves describe
assignments of probabilities (within intervals!) so Normal distributions are ______________
distributions. N(μ, σ) means that we are talking about a Normal distribution with __________
μ and standard deviation σ. In the language of random variables, if X has the N(μ, σ)
distribution, then the _________________ variable:
X 
Z

is a standard Normal random variable having the distribution N(0, 1).
YOU TRY:
1. Let the random variable X be a random number with the uniform density curve in Figure 7.5
(on previous pg.). Find the following probabilities.
a. P(X < 0.49)
b. P(X ≤ 0.49)
c. P(X ≥ 0.27)
d. P(0.27 < X < 1.27)
e. P(0.1 ≤ X ≤ 0.2 or 0.8 ≤ X ≤ 0.9)
f. The probability that X is not in the interval from 0.3 to 0.8
HW- pgs. 475-476 (7.8-7.10)
7.1 Quiz THURSDAY
Ch. 7 Test THURSDAY 12-22
www.westex.org
HS, Teacher Website
g. P(X = 0.5)