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ENGR 371 APPLIED STATISTICS AND PROBABILITY FOR ENGINEERS, 5TH CHAPTER 3 EDITION (DECEMBER 21)
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ENGR 371 APPLIED STATISTICS AND PROBABILITY FOR ENGINEERS, 5TH CHAPTER 3 EDITION (DECEMBER 21)
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ENGR 371 APPLIED STATISTICS AND PROBABILITY FOR ENGINEERS, 5TH CHAPTER 3 EDITION(DECEMBER 21)
th
Applied Statistics and Probability for Engineers, 5 edition December 21
CHAPTER 3
Section 3-1
3-4. The range of X is 0,1,2,3,4,5
3-7. The range of X is conveniently modeled as all nonnegative integers. That is, the range of X is 0,1,2,...
3-10. The possible totals for two orders are 1/8 + 1/8 = 1/4, 1/8 + 1/4 = 3/8, 1/8 + 3/8 = 1/2, 1/4 + 1/4 =
1/2,1/4 + 3/8 = 5/8, 3/8 + 3/8 = 6/8.
1 3 1 5 6
Therefore the range of X is , , , ,
4 8 2 8 8
Section 3-2
3-14.
f X (0) P( X 0)
f X (1.5) P( X 1.5)
f X (2)
f X (3)
a) P(X = 1.5) = 1/3
b) P(0.5< X < 2.7) = P(X = 1.5) +P(X = 2) = 1/3 + 1/6 = 1/2
c) P(X > 3) = 0
d) P(0 X 2) P( X 0) P( X 1.5) 1/ 3 1/ 3
e) P(X = 0 or X = 2) = 1/3 + 1/6 = 1/2
3-21. X = number of wafers that
3
passP(X=0) = (0.2) = 0.008
2
P(X=1) = 3(0.2) (0.8) = 0.096
2
P(X=2) = 3(0.2)(0.8) = 0.384
3
P(X=3) = (0.8) = 0.512
3-22. X: the number of computers that vote for a left roll when a right roll is
appropriate.p=0.0001.
4 4
P(X=0)=(1-p) =0.9999 =0.9996
3 3
P(X=1)=4*(1-p) p=4*0.9999 0.0001=0.0003999
2 2 2 -8
P(X=2)=C4 (1-p) p =5.999*10
3 1 3 -12
P(X=3)=C4 (1-p) p =3.9996*10
0 0 4 -16
P(X=4)=C4 (1-p) p =1*10
Section 3-3
3-35.
0, x 0
0.008, 0 x 1
F (x) 0.104, 1 x 2
0.488, 2 x 3
1, 3 x
, .
f (0) 0.23 0.008,
f (1) 3(0.2)(0.2)(0.8) 0.096,
f (2) 3(0.2)(0.8)(0.8) 0.384,
f (3) (0.8)3 0.512,
3-36.
.
0, x 0 f (0) 0.99994 0.9996,
0.9996, 0 x 1
f (1) 4(0.99993)(0.0001) 0.0003999,
F ( x) 0.9999, 1 x 3
f (2) 5.999 *10 8,
0.99999, 3 x 4
f (3) 3.9996 *10 12 ,
1, 4 x 16
f (4) 1*10
3-40. The sum of the probabilities is 1 and all probabilities are greater than or equal to
zero;pmf: f(1) = 0.7, f(4) = 0.2, f(7) = 0.1
a) P(X 4) = 0.9
b) P(X > 7) = 0
c) P(X 5) = 0.9
d) P(X>4) = 0.1
e) P(X 2) = 0.7
3-42. The sum of the probabilities is 1 and all probabilities are greater than or equal to
zero;pmf: f1/8) = 0.2, f(1/4) = 0.7, f(3/8) = 0.1
a) P(X 1/18) = 0
b) P(X 1/4) = 0.9
c) P(X 5/16) = 0.9
d) P(X>1/4) = 0.1
e) P(X 1/2) = 1
Section 3-4
3- 48. Mean and Variance for random variable in exercise 3-14
E( X ) 0 f (0) 1.5 f (1.5) 2 f (2) 3 f (3)
0(1/ 3) 1.5(1/ 3) 2(1/ 6) 3(1/ 6) 1.333
2
V(X ) 02 f (0) 1.52 f (1) 22 f (2) 32 f (3)
0(1/ 3) 2.25(1/ 3) 4(1/ 6) 9(1/ 6) 1.3332 1.139
3-56. (a) F(0)=0.17
Nickel Charge: X CDF
0 0.17
2 0.17+0.35=0.52
3 0.17+0.35+0.33=0.85
4 0.17+0.35+0.33+0.15=1
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