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xA2 Maths > Key Points > Flashcards

Key Points Flashcards

1
Q

What does ‘Mutually Exclusive’ mean?

A
  • That an event cannot occur at the same time as another event.
  • E.g: It is impossible to roll both a 5 and a 6 on a single dice at the same time.
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2
Q

Can two Mutually Exclusive events affect the probability of one another?

A
  • Yes, just because the events cannot occur at the same time, does not mean they have no effect on each other.
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3
Q

What is an independent event?

A
  • When an event has no influence over another event and is not influenced by another event.
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4
Q

What is a dependent event?

A
  • When the outcome of an event affects the outcome of another event, or when an event is affected by the outcome of another event.
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5
Q

When does the formula P(A∩B) = P(A) x P(B) hold?

A
  • When the events are independent.
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6
Q

When does the formula P(A∪B) = P(A) + P(B) hold?

A
  • When the events are mutually exclusive.
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7
Q

Give 3 ways of using graphical methods to solve probability questions:

A
  1. Venn Diagrams.
  2. Probability Trees.
  3. Sample Space Diagram.
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8
Q

What type of graph is more suitable than a bar chart when dealing with discrete data?

A
  • Line graph (skinny bar chart) is suitable for discrete data.
  • Because a bar chart contains a range of values normally, making it suitable for continuous data.
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9
Q

What type of data is the binomial distribution suitable for?

A
  • Discrete Data.
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10
Q

What do the 3 variables involved with Binomial Calculations represent?

A
  • N = number of trials.
  • P = probability of a trial being successful.
  • X = number of success’ (Probability you want to calculate.)
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11
Q

What is important about the sample size/number of trials when using a binomial distribution?

A
  • It is fixed. (n is a constant for each example)
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12
Q

Explain the initial setup for a Binomial Hypothesis test:

A
  • Define variables. (What is X)
  • Define Null Hypothesis: H0: p = x
  • Define Alternate Hypothesis: H1: P < x
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13
Q

What three variations can the alternate hypothesis take in a binomial hypothesis test?

A
  • H1: P < x (Less than)
  • H1: P > x (Greater than)
  • H1 : P ≠ x (Not equal to)
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14
Q

When dealing with an alternate hypothesis of > or <, what number of tails does the test have?

A
  • Single tailed test.
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15
Q

When dealing with an alternate hypothesis of ≠, how many tails does the test have?

A
  • Two tails. (Half significance level.)
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16
Q

What happens during the second half of a Binomial hypothesis test?

A
  1. Calculate the probability in question.
  2. Compare the probability to the significance level.
  3. If P < sig level, reject H0.
  4. If p > sig level, accept H0
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17
Q

Why is the method for working out the critical region for Binomial stupid?

A
  • You need to use trial and error. (Hence the stupidity.)
  • Use trial and error to find an X value which yields a probability less than the significance level.
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18
Q

When dealing with A2, what needs to be considered when working out probabilities?

A
  • Whether the two events in question are independent or dependant.
  • When events are dependent, you need to use the A2 formulae opposed to the AS formulae which assumes the events are independent.
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19
Q

What does the P(A∩B) equal when events are mutually exclusive?

A
  • When events are mutually exclusive the P(A∩B) = 0.
20
Q

What formulae always works for working out the P(A∪B)?

A
  • P(A∪B) = P(A) + P(B) - P(A∩B)
21
Q

What shape does a Normal Distribution create?

A
  1. Bell Curve.
  2. Symmetrical.
22
Q

What should always be done when dealing with Normal Distribution questions?

A
  • Draw a clear diagram.
23
Q

What is the Z distribution?

A
  • The Z Distribution has a mean of 0 and standard deviation of 1.
24
Q

What type of data does the Normal Distribution use?

A
  1. Continous.
25
Q

What does the letter ‘n’ represent when dealing with the Normal Distribution?

A
  • n = sample size.
26
Q

How does one start a normal distribution hypothesis test?

A
  1. Define Variables (X and μ)
  2. State a Null and alternate hypothesis.
27
Q

How do you calculate the sample mean from a normal distribution?

A
  • x ~ N(μ, σ2)
  • x̅ ~ N(μ, σ/n1/2 )
28
Q

What is the formula to work out a Z value for the Normal distribution?

A
  • Z = (X̄ -μ) / (σ/n1/2)
29
Q

What % of data lies within one standard deviation of the mean?

A
  • 68.27%
30
Q

What % of the data lies within 2 standard deviations of the mean?

A
  • 95.45% of the data lies within two standard deviations.
31
Q

What % of data lies within 3 standard deviations of the mean?

A
  • 99.73% of the data lies within 3 three standard deviations of the mean.
32
Q

What rule can easily be remembered regarding the correlation between data and standard deviations?

A
  • 68 - 95 - 99.7
33
Q

What does PMCC stand for?

A
  • Product Moment Correlation Coefficient.
34
Q

What PMCC value does perfect negative correlation have?

A
  • -1
35
Q

What PMCC value does perfect positive correlation have?

A
  • 1
36
Q

What PMCC value does a perfect lack of correlation have?

A
  • 0
37
Q

What letter is used to represent PMCC?

A
  • r
38
Q

What greek symbol is used to represent the PMCC of the parent population?

A
  • ρ
39
Q

Explain how the PMCC hypothesis test is carried out?

A
  • Define variables: (Let ρ be the PMCC of the….)
  • Define Null Hypothesis: (H0: ρ=0)
  • Define the Alternate Hypothesis: (H1: ρ<0)
  • Compare the value to the table.
  • Conclusion in context.
40
Q

What is the process called to convert binomial to normal?

A
  • Continuity Correction.
41
Q

How would one covert P(X=5) on a binomial, to a normal?

A
  • P(X=5) = 4.5
  • You take 0.5 either side of the value that you are trying to convert.
42
Q

How can one calculate the mean from a binomial distribution?

A
  • You need to work out the expected value, which is the mean.
  • E(X) = np.
  • Mean = number of trials x probability of success.
43
Q

How does one calculate standard deviation from a Binomial distribution?

A
  1. Variance = npq
  2. Variance = np(1-p)
  3. Variance = mean x probability of failure (1-p)
44
Q

In full form, how can a Binomial (B~(N,P)) be expressed as a Normal?

A
  • X~N((np),(np(1-p)))
45
Q
A

xA2 Maths (13 decks)

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