• Study Resource
• Explore

Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Gambler's fallacy wikipedia, lookup

Transcript
```Chapter 7
 Density
Curve
- A curve that describes the overall pattern
of a distribution.
- All Density Curves have and area of 1 or
100%
-Entire graph mush be above the x-axis
-Normal Distribution – Bell Shape N (  , )
-The area under the curve is the
proportion of observations that fall into that
interval
 Probability
 The
likelihood or chance that an event will
occur ranges from 0 to 1
-
The sum of all Outcomes in an experiment
is equal to 100%
A
quantity whose value changes.
 Today
you will learn about a few different
types of variables.
a
variable whose value is obtained by
counting
 Examples:
number of students present
 number of red marbles in a jar
 number of heads when flipping coins

a
variable whose value is obtained by
measuring
 Examples:
height of students in class
 weight of text books
 distance traveled between classes

a
variable whose value is a numerical
outcome of a random phenomenon
denoted with a capital letter, X
 can be discrete or continuous
 The probability distribution of a random
variable X tells what the possible values of X
are and how probabilities are assigned to
those values

A
coin is flipped 3 times and the sequence of
heads and tails are recorded. The sample
space for this experiment is:
 Let
the random variable X be the number of
heads in three coin tosses. Thus, X asigns
each outcome a number from the set
(0, 1, 2, 3).
Outcome
X
HHH
HHT
HTH
THH
HTT
THT
TTH
TTT
X
has a countable number of values.
 Probability
distribution of a discrete random
variable X lists the values and their
probabilities:
Value of
X
P(X)

0  P 1
 The
sum of the probabilities is 1
 What
is the probability distribution of the
discrete random variable X that counts the
number of heads in four tosses of a coin?
 The
number of heads, X, has possible values
0, 1, 2, 3, 4.
 These values are not equally likely!
P
(X = 0) =
 P(X
 P(
= 2)=
X > 1)=
P(X = 1) =
P(X = 3) =
P(X = 4) =
P( X  2) 
1. P(X < 4) =
2. P( x  2)
 NC
State posts the grade distributions for its
courses online. Students in Statistics 101 in
fall 2003 semester received 21% A’s, 43% B’s,
30% C’s 5% F’s, and 1% F’s. Choose a
Statistics 101 student at random. What is
the probability that the student got a B or
better?
 Less
than a C?
X
takes all values in a given interval of
numbers



The probability distribution of a continuous
random variable is shown by a density curve.
The probability that X is between an interval
of numbers is the area under the density
curve between the interval endpoints
The probability that a continuous random
variable, X is exactly equal to a number is
zero
 REMEMBER:
N(μ, σ) is our shorthand for a
normal distribution with mean μ and
standard deviation σ. So, if X has the N(μ, σ)
distribution then the we can standardize
using
Z
X

 An
opinion poll asks an SRS of 1500 American
adults what they consider to be the most
serious problem facing our schools. Suppose
30% say “drugs”. (We will learn about p̂ in
the next chapters, so for now go with it…) p̂  0.3
and N(0.3, 0.0118). What is the probability
that the poll results differs from the truth
about the population by more than two
percentage points?
 Let
“X” represent the sum of two dice
 A)
Define the random variables in this
situation.
 Is it a continuous or discrete random variable?
 Draw the density curve (ie: probability
distribution).
X
P(X)
2
3
4
5
6
7
8
9
10
11
12
1. P(X > 4) =
2. P( x  2)
```
Related documents