HW7 Solution
4.91 Let Y= water demand in the early afternoon. Then, Y is exponential with =100cfs.
= e-2 =.1353
a) P(Y>200) =
b) We require the 99th percentile of distribution of Y:
= e.99=.01 So, .99 = -100ln(.01)=460.52
P(Y>.99) =
4.96
a) Let
dy=1 so, k
HW6 Solution
4.47) The density for Y= delivery time is f(y)=1/4, 1<y<5.
Also, E(Y)=3, V(Y)=4/3
a. P(Y>2)=3/4
b. E(C)=E(c0+c1Y2)= c0+c1E(Y2)= c0+c1[V(Y)+(EY)2]= c0+c1[4/3+9]= c0+(31/3)c1
4.48) According to the definition of uniform probability distribution
HW5 Solution
3.72
.5
3.75
a. (0.9)^2 *0.1=0.081
b. 1-[0.9*0.1+0.1]=0.81
3.105
a. Y is not binomial because we are sampling without replacement from a small population.
b. Use the probability function for the hyper-geometric distribution, with N=8, n=3, r=
HW10 Solution
5.89
Cov(Y1,Y2)=E(Y1Y2)-E(Y1)E(Y2)=2/9-4/9=-2/9
As the value of Y1 increase, the value of Y2 tends to decrease.
5.91
E(Y1)=E(Y2)=2/3
E(Y1Y2)=
dY1dY2=4/9
So, cov(Y1,Y2) =E(Y1Y2)-E(Y1)E(Y2)=4/9-4/9=0 as expected since Y1 and Y2 are Independent
HW1 solution
2.10 a. S = cfw_A, B, AB, O
b. P(cfw_A) = 0.41, P(cfw_B) = 0.10, P(cfw_AB) = 0.04, P(cfw_O) = 0.45.
c. P(cfw_A or cfw_B) = P(cfw_A) + P(cfw_B) = 0.51, since the events are mutually
exclusive.
2.19 a. (V1, V1), (V1, V2), (V1, V3), (V2, V1), (V
Meilan Chen
Assignment Discrete Probability 1 due 09/16/2015 at 11:57pm EDT
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use a calculator if you want.)
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Material To Review for Midterm Exam #1
General Instructions
For each topic, review the material covered in class, homework problems, and
related exercises. When applicable, also review applications to coin tossing, dice rolling,
and card games such as pok
Material To Review for Midterm Exam #2
General Instructions
For each topic, review the material covered in class, homework problems, and related
exercises. All chapter, section, and page numbers refer to the course text, A First Course
in Probability by S
HW2 Solution
2.72 Note that P(A) = 0.6 and P(A|M) = .24/.4 = 0.6. So, A and M are independent.
Similarly, P( A | F ) = .24/.6 = 0.4 = P( A ), so A and F are independent.
2.76 Define the events:
U: job is unsatisfactory
A: plumber A does the job
a. P(U|A)