Purdue University Statistics 511: Practice Problems for Chapters 1-3, Study notes of Data Analysis & Statistical Methods

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Devore: Chapters 1-3 Practice Problems

Aug, 2006

Purdue University

Chapter 1, Pr. 22

A very large percentage of the data values are greater than

,

the end of the race.which indicates that most, but not all, runners do slow down at

some runners slow down a lot compared to the others.The histogram is also positively skewed, which means that

faster than they did the first 5 km is very small, about 1% or so.seconds. The proportion of the runners who ran the last 5 kmA typical value for this data would be in the neighborhood of 200

Aug, 2006

Purdue University

In general case, it becomes

[(

5 10 )

−

]

15 5 )

Now, we want to choose

of the

cordless,

of the

cellular,

and

of the corded phones:

2 5 )(

2 5 )(

2 5 )

15 6 )

Aug, 2006

Purdue University

Fall 2006

Chapter 2, Pr. 13

e

P

A

′ ∩

A

2 ′ ∩

A

3 ) =

P

A

3 ) −

P

A 1 ∩ A 3 ) − P

A 2 ∩ A 3 )

P

A 1 ∩ A 2 ∩ A 3

f

P

A

1 ′ ∩

A

2 ′ ) ∪

A

3 ) =

P

A

1 ′ ∩

A

2 ′ ∩

A

3 ′ ) +

P

A

3 )

P

A 1 ∪ A 2 ∪ A 3

P

A

3 )

P

A

1 ) +

P

A

2 ) +

P

A

3 ) −

P

A 1 ∩ A 2 )

P

A 1 ∩ A 3 ) − P

A 2 ∩ A 3 )

P

A 1 ∩ A 2 ∩ A 3

P

A

3 ) =

Aug, 2006

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Fall 2006

Problem 71, Chapter 2

Just note that

P

A

′ ∩

B

P

B

P

A

B

P

B

P

A

P

B

= [

P

A

)]

P

B

P

A

′ ) · P

(^) ( B

)

Aug, 2006

Purdue University

Problem 76, Chapter 2

The desired condition is

P

at least one opens

5

=

The next one is

P

at least one fails to open

5

=

Aug, 2006

Purdue University

Chapter 3, Pr. 33

Note that

E

X

∞

x ∑

x

· p ( x ) =

∞

x ∑

x

·

c

x 3

=

c

∞

x ∑

x 2

It is a well-known fact from the infinite series theory that

∞

x ∑

x 2

<

Aug, 2006

Purdue University

Chapter 3, Pr. 37

Note that

E

h ( X

E

X

6

x ∑

p ( x ) =

6

x ∑

x 1

At the same time,

1

3 . 5

=

Aug, 2006

Purdue University

Fall 2006

Chapter3, Pr. 58

Since

V

X

np

p )

the only values of

p

that turn the variance into zero are

and

.

Both correspond to the situation where nothing is random!

Take the derivative of

np

p ) with respect to

p

to put it equal

to zero to obtain

n

−

pn

This produces

p

= 0

.

Note that you need to verify that

p

= 0

is indeed the point of

maximum of the function

np

p ) .

Aug, 2006

Purdue University

Chapter 3, Pr. 83

λt For two-hour period the parameter of the distribution is

. Therefore,

P

X

e − 8 (^8)

10

For a

minute period,

λt

Therefore,

P

X

e − 2 (^2) 0

Clearly,

E

X

λt

Aug, 2006