1. Review of Important Concepts from STA247
Types of random variable (r.v) - discrete and continuous.
A discrete random variable has a probability mass function p(x).
A continuous random variable has a density function f(x).
Expectation…
Variance and standard deviation.
Covariance and correlation
i.i.d…
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2. Conditional probability and expectation. Distributions…
LLN – Law of Large Numbers
CLT – Central Limit Theorem
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3. Data and Statistics
Statistics is about data – collecting organizing, summarizing,
analyzing, using data to make decisions.
A statistic is a number in context.
Statistical inference is the connection between statistics and
probability.
There is a random mechanism behind the data because only have
data on a random sample or because there may be random
measurements error.
Data: observations x1, …, xn are considered n realizations of random variables X1,…, Xn or of 1 random variable X.
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4. Summarizing Data
Univariate statistics – consider only one variable at a time. We
colleted one measurement on n units.
Example: marks out of 100 on an exam were recorded for 20
students. Was it a hard exam?
How can we sensibly summarize the measurements?
We can summarize the data graphically and numerically and should
always report both types of summaries.
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5. Measure of Location and Center
The Mean or average of a data set x1, …, xn is given by
The mean is very sensitive to extreme observations.
Median – middle value of ordered observations. Unlike the mean,
the median is not sensitive to extreme observations. How to find
median?...
Mode – most common value. Note, the mode is not always a proper measure of center.
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6. The Five Numbers Summary
The five number summary consists of minimum, 1st quartile, median, 3rd quartile and maximum.
The 1st quartile is the value such that 25% of the data is less then or equal to it and 75% of the data is greater then it.
The 3rd quartile is the value such that 75% of the data is less then or equal to it and 25% of the data is greater then it.
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