INTRODUCTORY ECONOMETRICS – PROBABILITY – LECTURE 2 ...

INTRODUCTORY ECONOMETRICS – PROBABILITY – LECTURE 2 § Random experiment: a process leading to at least two possible outcomes with uncertainty as to which will occur o E.g. Toss a coin § Sample Space (population): The set of all possible outcomes of a random experiment o E.g. Sample space of tossing two coins [(HH),(TH),(HT),(TT)] § Event: A subset of the sample space o E.g. Define the event of tossing two coins; A = [(HT),(TH)] § Mutually Exclusive events: Events A and B have no common outcomes. § The occurrence of event A means that event B cannot occur o E.g. Draw a single card from a shuffled deck of cards § A = The event that the card is a King § B = The event that the card is a Queen § Collectively Exhaustive Events: A set of events which covers the entire sample space o E.g. Roll a single die § A = The event that the number is < 5 § B = The event that the number is > 2 § The Compliment of an Event: if A is an event from the sample space (population), then the compliment of A, denoted A’ is defined as shown: o E.g. Roll a single die § A = The event that the number < 5 § A’ = The event that the number is greater than or equal to 5 DEFINITIONS OF PROBABILITY

INTRODUCTORY ECONOMETRICS – STATISTICAL INFERENCE – LECTURE 4 POINT ESTIMATION § Y = Random variable § θ = A parameter of the PDF of Y § Y1, Y2 … YN = sample of observations on Y § A point estimator θˆ of the parameter θ = a function of Y1, Y2 … YN, that is designed §

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to be `close to' θ. To estimate the population mean [μ = E (Y)], draw an independent random sample of observations on Y, Y1, Y2 … YN, which we denote y1, y2, … yn & construct the sample mean shown: Add all Y values & divide by the sample size