## pwa quicklinks

This page provides better direct links to questions (with solutions inline, rather than on a separate page).

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For the 2017-18 of Probability with Applications.

**The philosophy** (as described by lecturer)

- The tutorial tasks are meant to help you understand the material covered in lectures (which follows selected parts of the textbook as indicated in lecture notes and slides) and help you deal with the subsequent Assignments. Please, do read the sections of the textbook which are discussed in lectures and try to solve the additional questions (but only those which are in those sections).
- You should make sure you understand all questions well enough to be able to deal with problems which might be formulated differently but are based on the same concepts.
- Exam:
- The exam questions WILL NOT go beyond the material covered in lectures and tutorials but bear in mind that the question formulation will be different from the ones in tutorials and assignments.
- Therefore you need to practice as much as possible (in order to be able to ‘map’ a given question onto what you have learnt). You will be examined on you familiarity with the covered material and NOT familiarity with the structure of questions in Tutorials and Assignments.

**Notes**

Asterisked questions or solutions are recorded to have mistakes. Others exist.

**Tutorials**

**Assessment Corrections**

*Assignment 9*

The solution states `π^3 = (0, 0, 1/4, 1/8, 0, 0, 1/2, 3/8)`

.
The second last entry `(1/2)`

is incorrect. It should be `(1/4)`

.

**Past Paper Solutions CORRECTED**

Avoid putting the answer at the start of entry to prevent spoilers (unless it affects the question)

- May 2018
**1(c)**: the correction calculation is indeed`15/56 - 15/64`

, but it comes out to`0.03348...`

, not the given`0.003`

**2(a)**: the answer is correct, but you might find it more natural to do`P(X=0)`

with the binomial distribution, which produces the exact same answer (`0.2084...`

)**3(e)**: the third P looks like`P([..] >= 1.95)`

. The arrow direction here is wrong. It should be`P([..] <= 1.95)`

. The answer is unaffected, it is just the direction of the arrows that are wrong.**6(d)**: don’t know if the answer is correct. the claim that “changing the limits from`1, 3`

to`1, 2`

does not change the result” is a mistake (so both lines are indeed not equal). BUT the requirement to change the limits is STILL NECESSARY- the reason the limits change is because we know
`XY < 1`

, we also know minimum value of Y is 0.5, so`0.5X < 1`

, therefore`X < 2`

- the reason the limits change is because we know
**7(a)**: the stated`P^2`

and`P^3`

are incorrect. This affects the*numbers*for the rest of 7(a). 7(b) and 7(c) are not affected by this mistake.**9(c)**: the stated`H(Y)`

has correct working out, but doesn’t evaluate to`1.436`

, it evaluates to`1.561...`

**10(a)**: Simple arithmetic error at the end,`1 - (5/6)`

is not equal to`1/5`

, it is equal to`1/6`

. Morons.