combinatory algebra A, let A[x] denote the set of expressions

given by the grammar

e ::= x | p aq | (ee)

where x is some fifixed symbol not in A and a ranges over the elements of A.

Given e ? A[x] and a ? A, let e[x := a] denote the element of A resulting from

interpreting occurrences of x in e by a, interpreting the expressions of the form

p a0 q by a0 and interpreting expressions of the form (ee0 ) using @.

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

e. [2 marks]

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

that

@(?xe, a) = e[x := a] (7)

for all a ? A. [6 marks]

(d) Recall the usual encoding of Booleans in ?-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 + ?)xt , and we would

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

(i) Find the maximum likelihood estimator for ? 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.

1_ _ is caused by math errors such as division by zero. a. NumberFormatException b.NullPointerException c.IOException d.ArithmeticException 2. Inheritance is one of the concept of OOPS. a.True b. False 3.byte is a primitive data type in Java. a. False b. True 4.What is the length of the array price in following declaration? double price = { 4.5, 5.2, 1.25, 60.0} a.5 b.4 c.3 d.ErrorDesign a "Book management system". Consider library has total 5 categories of books. Spiritual books, Comedy books, Story books, Horror books, Motivational books. A Book should include four pieces of information as book name, an ISBN number, an author name and a publisher. The librarian can issue books on rent. Rent of book depends on book category. (See Rent Details table). Design a system which performs following tasks using above OOPS Concepts. a) Design getter-setter for each property of book or complete method to Insert a new book. [Keep a record in an Array or static list] b) Fetch a list of books as per category. Print on screen or log into a file. c) Check whether the book is available or not. d) Take input for at least 5 customers for all different category books and print total rent for each customer. e) Use user interaction for above operations using the GUI or by simple commands. For example : Press 1 to insert a new book. ii) Press 2 to calculate the total rent for a book. Rent Details Book Rent per day Spiritual Book 10 Comedy 12 Story 8 Horror 15 Motivational 15