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"file": "UNB/Year 5/Semester 2/HIST3925/Lecture Notes.md", + "file": "UNB/Year 5/Semester 2/CS4725/Final Review.md", "mode": "source", "source": false }, "icon": "lucide-file", - "title": "Lecture Notes" + "title": "Final Review" } } ] @@ -168,10 +168,11 @@ }, "active": "a4868a0d0ec2cb3a", "lastOpenFiles": [ - "UNB/Year 5/Semester 2/CS4613/Lecture Notes.md", "UNB/Year 5/Semester 2/CS4725/Lecture Notes.md", - "UNB/Year 5/Semester 2/HIST3925/Breakout Questions.md", + "UNB/Year 5/Semester 2/CS4725/Final Review.md", "UNB/Year 5/Semester 2/HIST3925/Lecture Notes.md", + "UNB/Year 5/Semester 2/CS4613/Lecture Notes.md", + "UNB/Year 5/Semester 2/HIST3925/Breakout Questions.md", "UNB/Year 5/Semester 2/HIST3925/Guest Lecture Notes.md", "UNB/Year 5/Semester 2/HIST3925/Presentation Notes.md", "UNB/Year 5/Semester 2/CS3383/Lecture Notes.md", diff --git a/UNB/Year 5/Semester 2/CS4725/Final Review.md b/UNB/Year 5/Semester 2/CS4725/Final Review.md new file mode 100644 index 0000000..8dc87de --- /dev/null +++ b/UNB/Year 5/Semester 2/CS4725/Final Review.md @@ -0,0 +1,102 @@ +# Instructions: +12 FRQ, written answers +3 MCQ, multiple choice +1 Matching question, algorithms (role of algorithms) +15 total questions (?) + +1 A4 size double sided hand written notes allowed (Important!!!) +2 hour exam +Partial marks allowed for partially correct answers +Bring a calculator (Important!!!) +# Part 1 Important Questions +Horn form for logic? +Why are these conditions not solvable without a truth table? + +# Part 2 Important Questions +## 1 +Arithmetic assertions can be written in first order logic with the predicate symbol <, the function symbols + and x, and the constant symbols 0 and 1. Additional predicates can also be defined with bi-conditionals +a) Represent the property "x is and even number" +Ax Even(x) <=> Ey x=y+y +b) Represent the property "x is prime" +Ax Prime(x) <=> Ey,z x=y * z => y = 1 V z = 1 +c) Goldbach's conjecture is the conjecture (unproven as of yet) that "every even number is equal to the sum of two primes". Represent this conjecture as a logical sentence. +Ax Even(x)=> Ey,z Prime(y) /\ Prime(z) /\ x=y+z + +# 2 +Find the values for the probabilities a and b in joint probability table below so that the binary variables X and Y are independent + +| X | Y | P(X, Y) | +| --- | --- | ------- | +| t | t | 3/5 | +| t | f | 1/5 | +| f | t | a | +| f | f | b | +Due to probability being max 1, we know that a + b must be 1/5 +P(Yt)/P(Yf) = a/b = 3 +b = 1/20 +a = 3/20 + +# 3 +idk where R comes from, look into slides about bayes theorem +Show the three forms of independence in Equation (12.11) are equivalent +P(a|b) = P(a) or P(b|a) = P(b) or P(a /\ b) = P(a) * P(b) / R(?) + +First two are logically the same, just inverted + +From bayes theorem +P(a | b) * P(b) = P(a) * P(b) / R(?) + +P(a /\ b) = P(a | b) * P(b) + +# 4 +Consider the following propability distrobutions: + +| A | P(A) | +| --- | ---- | +| t | 0.8 | +| f | 0.2 | + +| A | B | P(B\|A) | +| --- | --- | ------- | +| t | t | 0.9 | +| t | f | 0.1 | +| f | t | 0.6 | +| f | f | 0.4 | + +| B | C | P(C\|B) | +| --- | --- | ------- | +| t | t | 0.8 | +| t | f | 0.2 | +| f | t | 0.8 | +| f | f | 0.2 | +Given these tables and no other assumptions, calculate the following probabilities. +a. P(a, ~b) + = P(a) * P(~b|a) + = 0.8 * 0.1 + = 0.08 +b. P(b) + = P(bt|a) * P(a) + P(bt | ~a) * P(~a) + = 0.9 * 0.8 + 0.6 * 0.2 + = 0.84 +# 5 +Let A and B be Boolean Random variables. You are given the following probabilities +P(A=true) = 0.5 +P(B=true |A=true) = 1 +P(B=true) = 0.75 + +What is P(B=true|A=false)? + +# 6 +Consider the XOR function of three binary input attributes, which produces the value 1 if and only if an odd number of the three input attributes has value 1. + +Draw a minimal sized decision tree for the three input XOR function. + +Three layer decision three, A > B > C. Output of tree would be +0 1 1 0 1 0 0 1 if on the left of the decision is always 0 and 1 is right + +# 7 +Consider the problem of separating N data points into +ve and -ve examples using a linear separator. Clearly this can always be done for N=2 points on a line of dimension d=1, regardless of how many points are labeled or where they are located (unless the points are in the same place) + +a) Show that it can always be done for N=3 points on a plane of dimension d=2 unless they are co-linear. + +b) Show that it cannot (or can we?) always be done for N=4 points on a plane of dimension d=2 \ No newline at end of file