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2. Fundamentals of Maths (CSC 1026) > Probability & Statistics > Flashcards

Flashcards in Probability & Statistics Deck (16)
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1

What are probability + statistics about?

These are both to do with analysing the situation where there are lots of related events.

2

What is probability?

Probability asks how likely it is that a certain event will happen.

3

What is statistics?

Statistics asks how to summarise all the events that happened.

4

What is the probability of an event happening?

The probability of an event happening is a real number in the range 0 (won’t happen) to 1 (will happen). If there are N trials + the event typically occurs M times, the probability of the event is M/N.

5

How do you represent situations which won't happen?

To represent situations which don’t happen, use Ā. The area of the circle represents the probability of A happening, the total probability of all events is 1, so the probability of A not happening, p(Ā) is 1 – p(A).

6

How do you calculate events which are equally likely to happen?

If there are N equally likely events which can happen during a trial, then the probability of any one of them is 1/N.

7

How do you calculate mutually exclusive events?

If A + B are mutually exclusive (can’t both happen), then adding their probability gives the probability of at least 1 happening (p(A) + p(B)). p(both) = 0.

8

How do you calculate independent events?

If A + B are independent events, A has no effect on whether B occurs. The probability that both of them will occur is p(A) * p(B). If we are looking for the probability that either one occurs, p(A) + p(B) – p(A) * p(B).

9

How do you test the probability of B if A already happened?
What about if A didn't happen?

p (B\A)
p (B\Ā)

10

How do you test the probability of B if A already happened + A + B are mutually exclusive?
What about if they're independent?

p (B\A) = 0. If A happened, B can’t.
p (B\A) = P(B).

11

What is the case if 2 events are dependent?

The first affects the second e.g. p (B\A) ≠ p(B)

12

What is a central measure?

Typical result.

13

What is the mean of a sequence of values?

If s is sequence of values, mean of s satisfies len(s) * mean(S) = sum of s(i) from i = 1 to len(s). Mean will be affected by extreme values even if just a few.

14

How do you calculate the median?

Less affected by extreme values. Middle value. At least half of the sequence elements are less than/equal to it + half are greater than/equal to it. Must satisfy (card ( { I | I ϵ (inds (s) · s (i) ≤ M } ) ≥ len (s) / 2) ^ (card ( { i | i ϵ inds (s) · s (i) ≥ M } ) ≥ len (s) /2)
To find median, we sort into asc order + choose middle value. If sequence even num, no central element + take mean of 2 central elements.

15

Hod do we calculate mode?

Most common. Must satisfy: ꓯ i ϵ inds (s) · card({x | ϵ inds (s) · s (x) = s(i)}) ≤ card ({z | ϵ inds (s) · s (x) = M})
To find mode, sort s into asc order, find which value occurs greatest num of times.

16

What is normal distribution?

Most values are somewhere near mean (bell curve).
Standard deviation of s a sequence of values: stdev(s) = calc mean of s, sum of squares of distances from mean, divided by len(s)-1 + take square root.