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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Tutorial Exercise

Suppose that we have a sample space

S = {E₁, E₂, E₃, E₄, E₅, E₆, E₇},

where

E₁, E₂, , E₇

denote the sample points. The following probability assignments apply:

P(E₁) = 0.05,

P(E₂) = 0.25,

P(E₃) = 0.25,

P(E₄) = 0.10,

P(E₅) = 0.20,

P(E₆) = 0.05,

and

P(E₇) = 0.10.

Let

A	=	{E₁, E₄, E₆}
B	=	{E₂, E₄, E₇}
C	=	{E₂, E₃, E₅, E₇}.

(a)

Find

P(A),

P(B),

and

P(C).

(b)

Find

A ∪ B

and

P(A ∪ B).

(c)

Find

A ∩ B

and

P(A ∩ B).

(d)

Are events A and C mutually exclusive?

(e)

Find

B^C

and

P(B^C).

Step 1

(a)Find

P(A),

P(B),

and

P(C).

Recall that an event is a collection of sample points, and the probability of an event is the sum of the probabilities of the sample points in the event. The sample points were given to be E₁, E₂, E₃, E₄, E₅, E₆, and E₇.

Event A is made up of the sample points E₁, E₄, and E₆. Thus, how can the probability of event A be determined?

P(E₁) + P(E₄) + P(E₆)

P(E₂) + P(E₃) + P(E₅) + P(E₇)

Event B is made up of the sample points E₂, E₄, and E₇. Thus, how can the probability of event B be determined?

P(E₁) + P(E₃) + P(E₅) + P(E₆)

P(E₂) + P(E₄) + P(E₇)

Event C is made up of the sample points E₂, E₃, E₅, and E₇. Thus, how can the probability of event C be determined?

P(E₁) + P(E₄) + P(E₆)

P(E₂) + P(E₃) + P(E₅) + P(E₇)

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