Key Points Flashcards
What does ‘Mutually Exclusive’ mean?
- 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.
Can two Mutually Exclusive events affect the probability of one another?
- Yes, just because the events cannot occur at the same time, does not mean they have no effect on each other.
What is an independent event?
- When an event has no influence over another event and is not influenced by another event.
What is a dependent event?
- When the outcome of an event affects the outcome of another event, or when an event is affected by the outcome of another event.
When does the formula P(A∩B) = P(A) x P(B) hold?
- When the events are independent.
When does the formula P(A∪B) = P(A) + P(B) hold?
- When the events are mutually exclusive.
Give 3 ways of using graphical methods to solve probability questions:
- Venn Diagrams.
- Probability Trees.
- Sample Space Diagram.
What type of graph is more suitable than a bar chart when dealing with discrete data?
- 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.
What type of data is the binomial distribution suitable for?
- Discrete Data.
What do the 3 variables involved with Binomial Calculations represent?
- N = number of trials.
- P = probability of a trial being successful.
- X = number of success’ (Probability you want to calculate.)
What is important about the sample size/number of trials when using a binomial distribution?
- It is fixed. (n is a constant for each example)
Explain the initial setup for a Binomial Hypothesis test:
- Define variables. (What is X)
- Define Null Hypothesis: H0: p = x
- Define Alternate Hypothesis: H1: P < x
What three variations can the alternate hypothesis take in a binomial hypothesis test?
- H1: P < x (Less than)
- H1: P > x (Greater than)
- H1 : P ≠ x (Not equal to)
When dealing with an alternate hypothesis of > or <, what number of tails does the test have?
- Single tailed test.
When dealing with an alternate hypothesis of ≠, how many tails does the test have?
- Two tails. (Half significance level.)
What happens during the second half of a Binomial hypothesis test?
- Calculate the probability in question.
- Compare the probability to the significance level.
- If P < sig level, reject H0.
- If p > sig level, accept H0
Why is the method for working out the critical region for Binomial stupid?
- 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.
When dealing with A2, what needs to be considered when working out probabilities?
- 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.
What does the P(A∩B) equal when events are mutually exclusive?
- When events are mutually exclusive the P(A∩B) = 0.
What formulae always works for working out the P(A∪B)?
- P(A∪B) = P(A) + P(B) - P(A∩B)
What shape does a Normal Distribution create?
- Bell Curve.
- Symmetrical.
What should always be done when dealing with Normal Distribution questions?
- Draw a clear diagram.
What is the Z distribution?
- The Z Distribution has a mean of 0 and standard deviation of 1.
What type of data does the Normal Distribution use?
- Continous.
What does the letter ‘n’ represent when dealing with the Normal Distribution?
- n = sample size.
How does one start a normal distribution hypothesis test?
- Define Variables (X and μ)
- State a Null and alternate hypothesis.
How do you calculate the sample mean from a normal distribution?
- x ~ N(μ, σ2)
- x̅ ~ N(μ, σ/n1/2 )
What is the formula to work out a Z value for the Normal distribution?
- Z = (X̄ -μ) / (σ/n1/2)
What % of data lies within one standard deviation of the mean?
- 68.27%
What % of the data lies within 2 standard deviations of the mean?
- 95.45% of the data lies within two standard deviations.
What % of data lies within 3 standard deviations of the mean?
- 99.73% of the data lies within 3 three standard deviations of the mean.
What rule can easily be remembered regarding the correlation between data and standard deviations?
- 68 - 95 - 99.7
What does PMCC stand for?
- Product Moment Correlation Coefficient.
What PMCC value does perfect negative correlation have?
- -1
What PMCC value does perfect positive correlation have?
- 1
What PMCC value does a perfect lack of correlation have?
- 0
What letter is used to represent PMCC?
- r
What greek symbol is used to represent the PMCC of the parent population?
- ρ
Explain how the PMCC hypothesis test is carried out?
- 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.
What is the process called to convert binomial to normal?
- Continuity Correction.
How would one covert P(X=5) on a binomial, to a normal?
- P(X=5) = 4.5
- You take 0.5 either side of the value that you are trying to convert.
How can one calculate the mean from a binomial distribution?
- You need to work out the expected value, which is the mean.
- E(X) = np.
- Mean = number of trials x probability of success.
How does one calculate standard deviation from a Binomial distribution?
- Variance = npq
- Variance = np(1-p)
- Variance = mean x probability of failure (1-p)
In full form, how can a Binomial (B~(N,P)) be expressed as a Normal?
- X~N((np),(np(1-p)))
