Question A.

If a keyboard operator averages 2 errors per page of newsprint and if these errors follow a Poisson process, what is the probability that

a. exactly 4 errors will be found on a given page?

b. at least 2 errors will be found on a given page?

2. Crossville police records show that there has been an average of 4 accidents per week on

Crossville's new freeway. If these accidents follow a Poisson process, what's the probability that

a. the police must respond to exactly 6 accidents in a week?

b. that the police must respond to fewer than two accidents in a week?

3. Bigrig Trailer Corporation uses large panels of sheet metal in the manufacture of tandem trailers. If there is an average of 3 blemishes per panel and if the blemishes follow a Poisson process, what is the probability that

a. there will be no blemishes on a given panel?

b. there will be exactly 2 blemishes on a given panel?

4. The student health center at Oklahoma State University in Stillwater treats an average of 10 cases of severe alcohol poisoning a semester. Assuming a Poisson distribution, find the probability that

a. that the health center treats twelve cases of severe alcohol poisoning a semester.

b. the health center treats fewer than 5 cases of severe alcohol poisoning a semester.

c. the health center treats more than 15 cases of severe alcohol poisoning a semester.

What are the current trends and innovation in geotechnical engineering specifically on site investigation?

2. What are the current trends and innovation in geotechnical engineering specifically on laboratory testing and analysis?

3. What are the current trends and innovation in geotechnical engineering specifically on ground improvement methods?

4. What are the current trends and innovation in geotechnical engineering specifically on dealing with underground structures?

5. What are the current trends and innovation in geotechnical engineering specifically on dealing with offshore geotechnical structures?

6. What is geosynthetics? Give at least 3 application of it that is currently used?

7. What are some examples of geo environmental applications?

(CO 3) Ten rugby balls are randomly selected from the production line to see if their shape is correct. Over time, the company has found that 89.4% of all their rugby balls have the correct shape. If exactly 6 of the 10 have the right shape, should the company stop the production line? Yes. as the probability of six having the correct shape is not unusual W/No. as the probability of six having the correct shape is unusual W/Yes, as the probability of six having the correct shape is unusual No. as the probability of six having the correct shape is not unusualLet Y1, . .. , Yn ~ Poi(1), for n = 1, 2, ... . Show that Xn = In - n D, N (0, 1), VIn as n - too, where T, = > Y, the sample total based on a sample of size n. That is, show i=1 that the limiting distribution of X, is the standard normal distribution. HINT: Re-write X, as Xn = AnZn, for some RVs An and Zn. Then apply the theorems in Sections 5.1 and 5.2, on pp. 289-300 of textbook, possibly in conjunction with the Weak Law of Large Numbers and the Central Limit Theorem, to show that An + 1 and Zn N (0, 1), as n + +oo.18. Suppose goods X and Y are produced along a production possibilities frontier 4X* + Y' = 500 and they are perfect substitutes such that U = X + Y. The slope of the production possibilities -4X frontier is How much X should be produced? 500 - 4X- a. b. 5 c. 10 d. 20 ANS: b 19. Suppose goods X and Y are produced along a production possibilities frontier 4X* + Y' = 500 and they are perfect substitutes such that U = X + Y. The slope of the production possibilities -4X frontier is How much Y should be produced? 500-4X- a. 5 C. 10 20 ANS: d