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
dy=1 so, k
4.47) The density for Y= delivery time is f(y)=1/4, 1<y<5.
Also, E(Y)=3, V(Y)=4/3
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
a. (0.9)^2 *0.1=0.081
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=
As the value of Y1 increase, the value of Y2 tends to decrease.
So, cov(Y1,Y2) =E(Y1Y2)-E(Y1)E(Y2)=4/9-4/9=0 as expected since Y1 and Y2 are Independent
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
2.19 a. (V1, V1), (V1, V2), (V1, V3), (V2, V1), (V
Assignment Discrete Probability 1 due 09/16/2015 at 11:57pm EDT
In the case above you need to enter a number, since were
testing whether you can multiply out these numbers. (You can
use a calculator if you want.)
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Material To Review for Midterm Exam #1
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
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
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