Math 89_Session 5

7/24/2019 Math 89_Session 5

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Random Variable and

Probability Distribution

MATH 89-EA

DEXBY P. DE GUZMAN, Ch.E.

Probability and Statistics for Engineersand Scientists by Walpole et al.


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Quiz on Probability

Random Variable

Probability Distribution(s)

Discrete

Continuous

Cumulative

TODAY:


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RANDOM VARIABLE

DISCRETE AND CONTINUOUS DATA


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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


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DISCRETE PROBABILITY

DISTRIBUTION (PMF)


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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.


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EXAMPLE 1: Probability mass function

plot


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EXAMPLE 1: Probability histogram


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EXAMPLE 1: Discrete cumulative

distribution function


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EXAMPLE 1: Discrete cumulative

distribution function


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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.


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CONTINUOUS PROBABILITY

DISTRIBUTION (PDF)


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Typical density functions


DISTRIBUTION (PDF)


14/19P(a < X < b)


DISTRIBUTION (PDF)


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EXAMPLE 3


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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)


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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


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REFERENCE

Walpole, Ronald E., et al. Probabil ity andStatistics for Engineers and Scientists .

Boston: Pearson Education, Inc., 2012.


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Thank You!

Documents

Math 89_Session 5