math 89_session 5
TRANSCRIPT
-
7/24/2019 Math 89_Session 5
1/19
Random Variable and
Probability Distribution
MATH 89-EA
DEXBY P. DE GUZMAN, Ch.E.
Probability and Statistics for Engineersand Scientists by Walpole et al.
-
7/24/2019 Math 89_Session 5
2/19
Quiz on Probability
Random Variable
Probability Distribution(s)
Discrete
Continuous
Cumulative
TODAY:
-
7/24/2019 Math 89_Session 5
3/19
RANDOM VARIABLE
DISCRETE AND CONTINUOUS DATA
-
7/24/2019 Math 89_Session 5
4/19
DISCRETE AND CONTINUOUS DATA
1. Number of red M&Ms in a pouch.DISCRETE
2. Number of traffic accidents in Cagayan
de Oro in one day. DISCRETE
3. Weight of babies at birth. CONTINUOUS4. Height of sea grasses in a particular bay.
CONTINUOUS
5. Time needed to travel from Camiguin to
Lagonglong. CONTINUOUS
6. Number of throws required to score 6
with a single dice. DISCRETE
-
7/24/2019 Math 89_Session 5
5/19
DISCRETE PROBABILITY
DISTRIBUTION (PMF)
-
7/24/2019 Math 89_Session 5
6/19
EXAMPLE 1
If a car agency sells 50% of its inventory of acertain foreign car equipped with side airbags,
find a formula for the probability distribution of
the number of cars with side airbags among the
next 4 cars sold by the agency.
-
7/24/2019 Math 89_Session 5
7/19
EXAMPLE 1: Probability mass function
plot
-
7/24/2019 Math 89_Session 5
8/19
EXAMPLE 1: Probability histogram
-
7/24/2019 Math 89_Session 5
9/19
EXAMPLE 1: Discrete cumulative
distribution function
-
7/24/2019 Math 89_Session 5
10/19
EXAMPLE 1: Discrete cumulative
distribution function
-
7/24/2019 Math 89_Session 5
11/19
DISCRETE PROBABILITY
DISTRIBUTION
EXAMPLE 2A shipment of 20 similar laptop computers
to a retail outlet contains 3 that are
defective. If a school makes a random
purchase of 2 of these computers, find the
probability distribution for the number ofdefectives.
-
7/24/2019 Math 89_Session 5
12/19
CONTINUOUS PROBABILITY
DISTRIBUTION (PDF)
-
7/24/2019 Math 89_Session 5
13/19
Typical density functions
CONTINUOUS PROBABILITY
DISTRIBUTION (PDF)
-
7/24/2019 Math 89_Session 5
14/19P(a < X < b)
CONTINUOUS PROBABILITY
DISTRIBUTION (PDF)
-
7/24/2019 Math 89_Session 5
15/19
EXAMPLE 3
-
7/24/2019 Math 89_Session 5
16/19
1. Find the probability distribution for the number of jazzCDs when 4 CDs are selected at random from a collection
consisting of 5 jazz CDs, 2 classical CDs, and 3 rock CDs.
Tasks:
a) Identify your random variable.b) Draw a tree diagram showing all the possibilities.
c) Construct a probability table.
d) Construct a probability histogram.
e) Repeat the tasks a-d if selection is done with
replacement.
Note: random variable on the horizontal axis and
probability on the vertical axis.
ASSIGNMENT (Short newsprint or bond paper)
-
7/24/2019 Math 89_Session 5
17/19
2. The proportion of people who respond to a certain mail-
order solicitation is a continuous random variable X that
has the density function
a) Show that P(0 < X < 1) = 1.b) Find the probability that more than 1/4 but fewer than
1/2 of the people contacted will respond to this type of
solicitation.
ASSIGNMENT
-
7/24/2019 Math 89_Session 5
18/19
REFERENCE
Walpole, Ronald E., et al. Probabil ity andStatistics for Engineers and Scientists .
Boston: Pearson Education, Inc., 2012.
-
7/24/2019 Math 89_Session 5
19/19
Thank You!