Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
Applied Statistics and Probability for Engineers, 7th edition 2017
4.7.16 Let X denote the time between two consecutive arrivals.
4.8.4 Let X denote the pounds of material to obtain 15 particles. Then, X has an Erlang distribution with r = 15 and
= 0.01.
4.8.5 a) Let X denote the number of customers that arrive in 10 minutes. Then, X is a
4.8.6 Let X denote the time until 5 messages arrive at a node. Then, X has an Erlang distribution with r = 5 and
= 30
messages per minute.
4.8.7 Let X denote the number of patients arrive at the emergency department. Then, X has a Poisson distribution with
= 65
patients per hour.
4.8.9 a) Mean of 1.74 particles per 200 nanoseconds.
Applied Statistics and Probability for Engineers, 7th edition 2017
4.8.11 Let X denote the time delay.
Section 4.9
4.9.1 If X is a Weibull random variable with
= 1 and
= 1000, the distribution of X is the exponential distribution with
4.9.4 Let X denote lifetime of a bearing.
= 2 and
= 10,000 hours.
a)
− −
= − = = =
2
8000
2 0.8
10000
( 8000) 1 (8000) 0.5273
X
P X F e e
4.9.6
= + =
1
( ) (1 ) 2.5
EX
Applied Statistics and Probability for Engineers, 7th edition 2017
4.9.10 a)
= = + =
1
( ) 1 16.01EX
4.9.11
=
( 26) 0.01
PX
4.9.12 Let X denote the average annual losses (in billions of dollars)
a)
= − = − = − − − =
0.8472
2
( 2) 1 ( 2) 1 (2) 1 1 exp 0.357
1.9317
P X P X F
Applied Statistics and Probability for Engineers, 7th edition 2017
Section 4.10
4.10.1 X is a lognormal distribution with
= 5 and
2 = 9
2 = 4
4.10.3 X is a lognormal distribution with
= 0.5 and
2 = 1
4.10.4 Find the values of
and
2 given that E(X) = 100 and V(X) = 85,000
Applied Statistics and Probability for Engineers, 7th edition 2017
4.10.5 a) Find the values of
and
2 given that E(X) = 10,000 and
= 20,000.
++
= = −
2 2 2
/2 2 2
10,000 20,000 ( 1)e e e
4.10.6
= + =
2
( ) exp( / 2) 120.87EX
4.10.7 X has a lognormal distribution with
= 1.5 and
= 0.4.
4.10.8 Let X denote the particle-size distribution (in centimeters).
4.10.10 Let X denote the levels of 2,3,7,8-TCDD in human adipose tissue.
( )
= = + =
2
( ) exp / 2 8
EX
Section 4.11
4.11.1 a)
−−
+
= −
0.25
11
0
()
( 0.25) ) (1 )
( ) ( )
P X x x
4.11.2 The probability density is symmetric.
Applied Statistics and Probability for Engineers, 7th edition 2017
4.11.3 a)
−
= = =
+ − + −
12
Mode 0.8333
2 3 1.4 2
4.11.4 a)
−−
+
= −
1
11
0.9
()
( 0.9) ) (1 )
( ) ( )
P X x x
4.11.5 Let X denote the completion proportion of the maximum time.
4.11.6
= = =
+
( ) 0.3EX
, then
= 2.33
4.11.7
a)
− − − − − −
= = =
− − − −
( )(2 ) (1.333 1)(2(1.25) 1 2) 2
( )( ) (1.25 1.333)(2 1)
a m a b
m b a
Applied Statistics and Probability for Engineers, 7th edition 2017
c)
Supplemental Exercises
4.S8 f(x) = 0.04 for 50< x <75
4.S9 a)
−
= = − =
45 60
( 45) ( 3) 0.00135
5
P X P Z P Z
4.S10 a)
−−
= = − −
50 100 80 100
(50 80)
( 2.5 1)
P X P Z P
Z
4.S11 E(X) = 1000(0.2) = 200 and V(X) = 1000(0.2)(0.8) = 160
4.S12 The time to failure (in hours) for a laser in a cytometry machine is modeled by an exponential distribution with 0.00004.
4.S13 Let X denote the number of calls in 3 hours. Because the time between calls is an exponential random variable, the
4.S14 a)
= + =
2
( ) exp( / 2) 0.001EX
4.S15 Let X denote the lifetime
4.S16 Let X denote the time between calls. Then,
==1/ ( ) 0.1EX
calls per minute.
Applied Statistics and Probability for Engineers, 7th edition 2017
4.S18 X is a lognormal distribution with
= 0 and
2 = 4
a)
= =
(10 50) (10 50) (ln(10) ln(50))
W
P X P e P W
4.S19 a) Find the values of
and
2 given that E(X) = 50 and V(X) = 4000
Applied Statistics and Probability for Engineers, 7th edition 2017
4.S20 Let X denote the number of fibers visible in a grid cell. Then, X has a Poisson distribution and
= 100 fibers per cm2.
4.S21 a) X follows an exponential distribution with
= 1/3
4.S22 a) Let X denote the dot diameter. If P(0.0014 < X < 0.0026) = 0.9973, then
4.S23
a) Using the normal approximation to the binomial with n = 50(36)(36) = 64,800 and p = 0.0001 we have E(X) =
4.S24 Using the normal approximation to the binomial with X being the number of people who will be seated.
4.S26
a)
4.S28
a)
=
= 0.5 < 1
b)
=
= 1
The function is symmetric and there are no peaks. Actually, this probability density function is the same as the standard
uniform distribution.
Applied Statistics and Probability for Engineers, 7th edition 2017
4.S29
=
−=
2500
(1 ) 43.3
np
np p
4.S30 Let X denote the time interval between filopodium formation.
4.S32 Let X denote the survival time of AMI patients.
a)
(shape parameter)
