Amanda has a von Neumann-Morgenstern utility function given by U= VM , where Mis her income. If she becomes an economics professor, she will make M- 64/yr with probability 1. If she becomes an attorney, she will make M= 900/yr if she becomes a partner in a Wall Street firm, but only M 49/yr if she fails to make partner. The probability of her becoming a partner is 0.3. Ellis is an infallible Judge of legal talent. After a brief interview, he can state with certainty whether Amanda will become a partner. What is the most Amanda would be willing to pay for this information? (Set up the relevant equation and solve it.) Instructions: Round your answer to 2 decimal places.

Show work for every step. Two types of customers (Preferred and Regular) call a service center. Preferred customers call with rate 3 per hour, and Regular customers call with rate 5 per hour. The interarrival times of the calls for each customer type are exponentially distributed. If the call center opens at 8:00 AM, what is the probability that the first call (regardless of customers type who calls) is received before 8:15 AM?

Sarah and Thomas are going bowling. The probability that Sarah scores more than  175  is  0.5 , and the probability that Thomas scores more than  175  is  0.1 . Their scores are independent. Round your answers to four decimal places, if necessary.   (a) Find the probability that both score more than  175 .   (b) Given that Thomas scores more than  175 , the probability that Sarah scores higher than Thomas is  0.4 . Find the probability that Thomas scores more than  175  and Sarah scores higher than Thomas.

For the M/M/N/o system, the probability that an arrival will find all servers busy and will be forced to wait in queue is an important measure of performance of the M/M/N/∞ system. This probability is given by PQ N!(1 – p/N) | and is known as the Erlang C formula. Please derive the equation. What is the expected number of customers waiting in the queue (not in service)?

Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like?         a. The area in the right tail of the standard normal curve.   b. The area not including the right tail of the standard normal curve.…

From observations of the weather, it is known that on October 20 the probability of rain is 0.85. A certain forecast method for October 20 is correct  0.9 times if rain is predicted and 0.75 times if no rain is predicted.  How much information does a real weather forecast provide 20 th of October? n.b the picture is example of solution

A student goes to the library. Let events B=B= the student checks out a book and D=D= the student check out a DVD. Suppose that P(B)=0.59PB=0.59, P(D)=0.45PD=0.45 and P(D|B)=0.50PD|B=0.50. Round each answer to four decimal places.  Find P(B′) Find P ( D and B) Find P (B\D) Find P (D and B') Find P (D\B')