Question Solved1 Answer 1. Let A and B be events such that P(A) = 0.42 and P(B) = 0.4. Find P(AB) assuming (a) A and B are mutually exclusive. (b) A and B are statistically independent.

Let {X1,..., Xn} be independent random variables with mean zero and let (a1, ..., an) ER”. (a) Sub-exponential random variable [1 pt] Compute bounds for Pla;X;| 2 t) n i=1 under the assumption that the Xi's are in (v2, a)-sub-exponential. (b) Sub-Gaussian random variable (1 pt] Compute bounds for P(IΣαX;| Σt) n i=1 under the assumption that the X;'s are in o2-sub-Gaussian.

Q.17: Heat in the amount of 7.5 kJ is added to a closed system while its internal energy decreases by 12 kJ. How much energy is transferred as work? For a process causing the same change of state but for which the work is zero, how much heat is transferred?

Blue Spruce Corp. has decided to expand its operations. The bookkeeper recently completed the following statement of financial position in order to obtain additional funds for expansion:obligation is considered a long-term liability. (List Current Assets in order of liquidity. List Property, Plant and Equipment in order of Buildings, and Equipment.)

(15 points): Consider (again) the complex function G: C+C defined by 8 +2 G(8) 32 +63 + 18 (a) By hand, draw a pole-zero map of G (i.e., in the complex plane, draw a "o" to indicate points where G evaluates to zero and an "x" to indicate points where the magnitude of G tends to infinity).

The problem is Customers arrive at a tool crib according to a Poisson process of rate $\lambda = 5$ per hour. There is a single tool crib employee, and the individual service times are exponentially distributed with a mean service time of 10 minutes. In the long run, what is the probability that two or more workers are at the tool crib being served or waiting to be served? It is given that $\lambda = 5$, and I believe that $\mu = 6$ customers per hour. Then, I think the answer is $$1-\frac{1}{6}-\frac{1}{6}\left(\frac{5}{6}\right)-\frac{1}{6}\left(\frac{5}{6}\right)^2 = \frac{125}{216}.$$ However, the answer in the back is $\frac{25}{36}$. I was wondering what I did wrong. Or is the answer in the back wrong? Thanks.

26. EMPLOYEE POPULATION BASE In a large metropolitan area, 81% of the employed population is enrolled in a health maintenance organization (HMO). If 700,650 employees are enrolled, find the total number of people in the employed population. 28. VOTER REGISTRATION Registered Republican voters make up 13.8% of the population of one county, If there are 345,000 registered Republican voters in the county, find the total population in the county 30. DRIVING TESTS In analyzing the success of driver's license applicants, the state finds that Sa 3% of those examined received a passing mark. If the records show that 8370 new driver's licenses were issued, what was the number of applicants? Round to the nearest whole number 32. FAMILY SIZE One survey among college students found that 28.4% grew up in a home with two or more siblings and 44.7% grew up in a home with one sibling. If 194 students grew up in a home with no siblings, find the size of the survey group 34. HIRING Apple, Inc. recently announced that it will be hiring 5000 employees. If this is about 4.3% of the current workforce, estimate the number of people who work for Apple. 36. SMOKING OR NONSMOKING A casino hotel in Barbados states that 70% of its rooms are for nonsmokers. If the resort allows smoking in 264 rooms, find the total number of rooms. 22. JOB CUTS One Carrier Corporation factory builds air conditioning systems for commercial buildings. Sales are traditionally low as summer draws to an end and the manager decides he must lay off 80 of the 760 employees working on the assembly lines. Find the percent of workers that will be laid off. 24. VOCABULARY There are 55,000-plus words in Webster's Dictionary, but most educated people can identify only 20,000 of these words. What percent of the words in the diction-ary can these people identify 26. TANNING SALON Only 250 of Thai Beach's 1100 customers tan regularly. Find the per cent that tan regularly 28. MOTORCYCLISTS Of the 2380 motorcycle riders that participated in a recent bike rally through the California mountains, 2041 were men. Find the percent who were men. 30. WIND ENERGY In the early 1980s, wind-generated electricity cost about 30 cents per kilo-watt hour. Today, the best wind systems can produce electricity for 2 cents per kilowatt hour Find today's cost as a percent of the cost in the 1980s. p104 4,6 4. GLOBAL WARMING Periodically, 50% or more of all species of animals have gone extinct in a relatively short period of time. Many scientists believe we are entering such a period now as Earth warms. In fact, one scientist predicts that as many as 5 million out of the estimated 8.7 million species on Earth will disappear by 2100. Find the percent that may go extinct 6. LIGHTS OUT There are still 88,000 households in the United States that do not have electricity. If this is 08% of the homes, find the total number of households.