A specific kind of apparatus can breakdown from one of two potential sorts of disappointments. To evaluate whether a breakdown is because of the primary sort costs C1 dollars. In the event that that kind caused the breakdown, the maintenance costs R1 dollars. Also, the expense of surveying whether the breakdown is because of the subsequent kind is C2 dollars and, on the off chance that it is a disappointment of the subsequent sort, the maintenance cost is R2 dollars. The likelihood that the primary sort of disappointment caused the breakdown is p so (1 - p) is the likelihood that the second kind of disappointment caused the breakdown. In the event that one kind of disappointment is checked and discovered not to be the reason for the breakdown, the other sort of disappointment should in any case be checked before a maintenance should be possible. Under what conditions on p, C1, C2, R1, and R2 should the main kind of disappointment be checked first, instead of the second sort of disappointment being checked first, to limit the normal absolute expense of fix.

Question 50

A rancher recruits an expert to reveal to him whether he needs to splash his cotton harvest to control creepy crawlies. At whatever year, the likelihood that treatment is important to forestall genuine financial misfortune is 0.6. On the off chance that treatment is vital, the specialist suggests treatment 99% of the time. On the off chance that treatment isn't really important, the specialist suggests treatment 40% of the time. The rancher consistently follows the suggestion.

a What is the likelihood that the rancher will shower 3 years in a row? b The expense of showering is C. Without thinking about the expense of splashing, the rancher's benefit is P1 if no treatment is required or if treatment is given (regardless of whether it is required) and P, if treatment is required yet not given. Track down the normal worth of benefit, contemplating the expense of splashing over the 3 years.

Question 51

It is realized that 5% of the populace has sickness A, which can be found through a blood test. Assume that N (a huge number) individuals are tried. This should be possible twoly: 1 Each individual is tried independently. 2 The blood tests of k individuals are pooled together and investigated. (Accept that N = nk, with n a whole number.) If the test is contrary, the entirety of the people in the pool are sound (i.e., simply this one test is required). In the event that the test is positive, every one of the k people should be tried independently (i.e., a sum of k + 1 tests are required).

a For fixed k, what is the generally anticipated number of tests required in technique (2)? b Find the incentive for k that will limit the normal number of tests in strategy (2). c what number tests does part (b) save in correlation with section (a)?

Question 52

The quantity of rainstorm days in a year has been demonstrated utilizing a negative binomial model (Sakamoto 1973).A tempest day is characterized as a day during which in any event one tempest cloud (cumulonimbus) happens joined by lightning and thunder. It might be joined by solid whirlwinds, downpour, or hail. For one such site, the mean and difference of the quantity of tempest days are 24 days and 40 days2, individually. For an arbitrarily chosen year, complete the accompanying.

a Find the qualities for r and p. b Find the likelihood that there are no rainstorm days during a year. c Find the likelihood of at any rate two rainstorm days during a year.