Probability. P(6) = 1/6 = 0.1666 Sample space:1,2,3,4,5,6.
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Transcript of Probability. P(6) = 1/6 = 0.1666 Sample space:1,2,3,4,5,6.
![Page 1: Probability. P(6) = 1/6 = 0.1666 Sample space:1,2,3,4,5,6.](https://reader036.fdocuments.in/reader036/viewer/2022062320/56649d555503460f94a332a0/html5/thumbnails/1.jpg)
Probability
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Probability
P(6) = 1/6 = 0.1666
Sample space: 1,2,3,4,5,6
![Page 3: Probability. P(6) = 1/6 = 0.1666 Sample space:1,2,3,4,5,6.](https://reader036.fdocuments.in/reader036/viewer/2022062320/56649d555503460f94a332a0/html5/thumbnails/3.jpg)
Probability
• Probability values range from 0 to 1.
• Adding all probability of the sample yields 1.
• The probability that an event A will not occur is 1 minus the probability of A.
• If two events are independent, the probability is the sum of their individual probabilities.
• Two events A and B are independent if knowing that the occurrence of A does not change the probability of the occurrence of B.
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Probability
Law of large numbers
The larger the sample space, the closer the
sample distribution to the theoretical distribution.
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Joint Probability
P(5,6) = (0.166) P(0.166) = 0.0277
P(A,B) = P(A) P(B)
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Conditional Probability
P(AB ) =P(A B)
P(B)
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Conditional Probability
In a corpus including 12.000 nouns and 3.500
adjectives, 2.000 adjectives precede a noun.
(1) What is the likelihood that a noun occurs after
an adjective?
(2) What is the likelihood that an adjective
precedes a noun?
![Page 8: Probability. P(6) = 1/6 = 0.1666 Sample space:1,2,3,4,5,6.](https://reader036.fdocuments.in/reader036/viewer/2022062320/56649d555503460f94a332a0/html5/thumbnails/8.jpg)
Conditional Probability
P(ADJN) =P(ADJ N)
P(N)
P(ADJN) =P(2000)
P(12000)
P(NADJ) =P(2000)
P(3500)
= 0.1666
= 0.5714
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Probability
transitive
intransitive
pronominal
lexical
pronominal
lexical
0.4 0.8 = 0.32
0.4 0.2 = 0.08
0.6 0.6 = 0.36
0.6 0.4 = 0.24
Sum = 1
0.4
0.6
0.8
0.2
0.6
0.4
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Probability distribution
TH
HH HT TH TT
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Probability distribution
0 heads = HH
1 head = HT + TH
2 heads = TT
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Probability distribution
HH
HT
TH
TT
0
1
3
Sample space Random variable
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Probability distribution
Cumulative outcome
0 = 11 = 22 = 1
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Probability distribution
Cumulative outcome Probability
0 = 11 = 22 = 1
0.250.500.25
P(x) = 1
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Binomial distribution
• two possible outcomes on each trail
• the outcomes are independent of each other
• the probability ratio is constant across trails
Bernoulli trail:
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Binomial distribution
• It is based on categorical / nominal data.
• There are exactly two outcomes for each trail.
• All trials are independent.
• The probability of the outcomes is the same for each trail.
• A sequence of Bernoulli trails gives us the binominal distribution.
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Example 1
A coin is tossed three times. What is the probability of obtaining two heads?
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TH
HH HT TH TT
HHH HHT HTH HTT THH THT TTH TTT
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Sample space: HHH TTTHHT TTHHTH THTTHH HTT
Random variables: 0 Head1 Head2 Heads3 Heads
0 head: 11 head: 32 heads: 33 heads: 1
/ 8 = 0.125/ 8 = 0.375/ 8 = 0.375/ 8 = 0.125
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If you toss a coin 8 times what is the probability of obtaining a score of:
0 heads1 head2 heads3 heads4 heads5 heads6 heads7 heads8 heads
Example 2
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![Page 22: Probability. P(6) = 1/6 = 0.1666 Sample space:1,2,3,4,5,6.](https://reader036.fdocuments.in/reader036/viewer/2022062320/56649d555503460f94a332a0/html5/thumbnails/22.jpg)
Probability Distribution
Sample:Tossing a coin a 100 times, yielded 42
heads and 58 tails. Is this a fair coin?Heads: 42Tails: 58
Expected: 50% - 50%
Sample error?
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Samples42 : 58
Population4 : 4?
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Normal distribution
![Page 25: Probability. P(6) = 1/6 = 0.1666 Sample space:1,2,3,4,5,6.](https://reader036.fdocuments.in/reader036/viewer/2022062320/56649d555503460f94a332a0/html5/thumbnails/25.jpg)
Normal distribution
• The center of the curve represents the mean, median, and mode.
• The curve is symmetrical around the mean.
• The tails meet the x-axis in infinity.
• The curve is bell-shaped.
• The total under the curve is equal to 1 (by definition).
![Page 26: Probability. P(6) = 1/6 = 0.1666 Sample space:1,2,3,4,5,6.](https://reader036.fdocuments.in/reader036/viewer/2022062320/56649d555503460f94a332a0/html5/thumbnails/26.jpg)
Skewed distribution
![Page 27: Probability. P(6) = 1/6 = 0.1666 Sample space:1,2,3,4,5,6.](https://reader036.fdocuments.in/reader036/viewer/2022062320/56649d555503460f94a332a0/html5/thumbnails/27.jpg)
Bimodal distribution
![Page 28: Probability. P(6) = 1/6 = 0.1666 Sample space:1,2,3,4,5,6.](https://reader036.fdocuments.in/reader036/viewer/2022062320/56649d555503460f94a332a0/html5/thumbnails/28.jpg)
Skewed distribution
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Random distribution
![Page 30: Probability. P(6) = 1/6 = 0.1666 Sample space:1,2,3,4,5,6.](https://reader036.fdocuments.in/reader036/viewer/2022062320/56649d555503460f94a332a0/html5/thumbnails/30.jpg)
Normal distribution
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Example
Boys MLU Girls MLU
2.72.92.62.33.22.92.6
3.22.93.03.43.23.32.9
2.74 3.12
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Example
Inspection of data:
1. Frequency – ordinal –interval
2. Normally distributed – not normally distributed
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Boys 2.8
Girls 3.3
Boys
Girls