Probability Flashcards
What is Continuous Probability Distribution?
- probability distribution in which random variable X takes on any value + describes it {P(X = x) = 0}
- uses probability density function
What is the discrete probability distrubution?
probability distribution counts occurrences that have countable or finite outcomes
What are the features of a continuous distribution?
- normal distribution
- Uni-modal & symmetrical
- extreme values away from centre
What is the standard normal distribution for continuous distribution probability?
σ = 1, μ = 0
What happens when the mean is changed on a normal distribution?
The curve changes where it is centred on the x-axis
What happens when the standard deviation is changed on a normal distribution?
Adjusting σ changes the shape of the curve
List the properties of a normal distribution
- 68% -> 1 SD either side of mean
- 95% -> 2 SD either side of mean (1.96 exactly)
- 99.75% -> under 3 SD but extremely rare
What are the 3 properties of sampling distribution?
- variability in sample estimates
- higher sample size = less variable in samples -> more representative sample
- larger samples = point-estimate from samples are closer to population value
What is the difference between a smaller and larger standard error?
Large standard error = more distributed
Small standard error = grouped in one area; it’s closer to the population parameter
What happens when the number of samples increase?
- sampling distribution becomes normal
- samples x̄s pile around µ
- the SE of sampling distribution becomes narrower
What is the central limit theorem?
Taking large samples from a population, the sample mean will be normally distributed even if the population isn’t
What is analytic probability?
- Probability of event equal to ratio of successful outcomes to all possible outcomes
What is the law of large numbers?
- larger the number the more proportion represents ground truth, representing the world
What is the range probability rule and what does it mean?
- probability of any event falls between 0 and 1
- P(A) approaches 1 means more likely to occur
What is the Sum of outcomes probability rule and what does it mean?
- Sum of probabilities of all possible outcomes = 1
- all sample includes all possible outcomes of experiment so some outcomes must occur
What is the complement rule probability rule and what does it mean?
- Probability of A^c(NOT A) =1- probability of A
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What is the Simple addition rule probability rule and what does it mean?
- Probability one or both events occur
- adding probability of one event to another
- used for mutually exclusive events as can’t coexist together
What is the general addition rule probability rule and what does it mean?
- Probability one or both events occur when events not mutually exclusive
- Also used when events are mutually exclusive -> probability both occur together is 0
What is the multiplication rule probability rule and what does it mean?
- Probability of intersection of A and B if they are independent events.
- Probability of A and B always less than or equal to the probability of either single events
What is the conditional probability rule and what does it mean?
- The probability of one of the other happens
- Multiply probability of A with the probability of B given A
What is the conditioned probability?
Probability of B given A
- events are dependent on likelihood of one event changing based on the outcome of the other event
What is the difference between the conditioned probability and multiplication rule?
- When A and B are independent P(B|A) = P(B) is the simple multiplication rule BUT
conditioned probability when A and B are dependent
What is Bayes’ rule?
- Calculating conditional probabilities when intersection unknown
- Follow on from conditioned probability
- Allows update assessment of probability as more evidence gathered
What is a sample space?
All possible outcomes
