Give the clauses in a defifinition of e[x := a] by recursion on the structure of

e. 

(ii) For each e ∈ A[x] show how to defifine an element Λxe ∈ A with the property

that

@(Λxe, a) = e[x := a] (7)

for all a ∈ A. 

(d) Recall the usual encoding of Booleans in λ-calculus. Using Part (c)(ii), show

that in any combinatory algebra A there are elements True, False ∈ A and a

function If : A × A → A satisfying

@(If (a, b), True) = a

(11)

@(If (a, b), False) = b

(12)

for all a, b ∈ A

[5 marks]

7CST1.2021.6.8

7

Data Science

(a) Let xt be the number of new COVID infections on date t. We anticipate

approximately exponential growth or decay, xt+1 ≈ (1 + λ)xt , and we would

like to estimate λ from a dataset (x1, . . . , xT ).

(i) Find the maximum likelihood estimator for λ for the model

Xt+1 ∼ Poisson

 

Utilizing the data gave for the situation study, would you be able to assemble a Context graph, Level 0 Data Flow Diagram, and an ERD utilizing any outlining programming.

The 2020 Covid pandemic has affected numerous enterprises across the globe and Australia's organic product picking industry is no exemption. Natural product send out contributes fundamentally to Australia's exchange. Most natural products are by and large transitory and consequently natural product picking is something that should be done brilliantly and with care. In spite of the fact that Australia's organic product picking industry faces a few issues, one of them is absence of adequate labor. This issue, among many, has exasperated as of late because of COVID 19. To help the ranchers and the natural product picking industry, Zaf Soft, an Australian Information System supplier association has concocted an online arrangement that would assist with fruiting ranchers pick organic product well on schedule. The CEO of Zaf Soft, Rabee James has chosen to send off a site donesloching.com. The thought is basic, innovative and in particular it adds financial worth. donesloching.com would permit Australian ranchers and organic product pickers to enroll on this site. While ranchers can enlist separately, the site additionally permits bunch enrollment for organic product pickers. Natural product pickers are common individuals dwelling in Australia who wish to add to organic product picking. These individuals frequently wish to work/procure compensation or on occasion be essential for the organic product picking process for relaxation as it were. The enlistment cycle for the ranchers is basic. Ranchers give their contact subtleties, ranch address and above all; their business charge subtleties. This is went with a picture ID that is likewise given as a feature of the enlistment interaction. The organic product pickers give a lot of comparative subtleties in the event that they wish to do natural product picking for procuring an everyday, month to month or a time-based compensation. For this situation they additionally give bank subtleties while enlisting. As opposed to this, in the event that the natural product picker wishes to enroll for recreation just, bank subtleties and expense subtleties are not needed by the framework. Natural product picker's gathering enrollments is just conceivable assuming that the enlistment is for relaxation as it were. The site permits the natural product pickers to choose and plan their visits for natural product picking for a specific ranch; seven days ahead of time. Each mentioned plan is supported by the rancher and afterward the natural product pickers get endorsement warning by means of email or potentially as portable instant message (as solicitation by the natural product picker). Visits to the homestead without rancher's endorsement are not permitted and not upheld by the framework and the mentioned plan is auto declined in no less than multi week from the mentioned date if in any case not supported by the rancher. While mentioning for a timetable, the natural product pickers give subtleties of the fruit(s) that they need to pick. This is to guarantee the executives of wages, time, instrument and assets expected to play out the work action. Compensation differ with time, weight of organic product picked and the kind of organic product. The compensation is chosen according to the rancher's circumspection and is given by the rancher at the hour of enlistment

20% Basic Java 20% Control structures 20% Classes 10% Methods usage of comments next to the program variables declaration: input/output data types 10% Arrays decision: if else if.... Else switch... case (optional) repetition (at least 2 iterations) while, do...while for (at least 2 classes) (at least 2 methods) user-defined and/or built-in methods (at least 1 set of array) 20% User Interface Menu like starting point User friendliness Error free