# ODTU 206 - ECON 206 METU Department of Economics LECTURE 01...

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ECON 206 October 04, 2010 METU- Department of Economics Instructor: H. Ozan ERUYGUR e-mail: [email protected] 1 LECTURE 01 INTRODUCTION AND SAMPLING DISTRIBUTIONS Outline of today’s lecture: I. Refreshment: Relative Frequency Density and Probability Distribution . .......................... 1 II. Refreshment: Expected values (mathematical expectation) . ............................................. 6 A. Formula for mean and variance in terms of expected values . ....................................... 6 1. Discrete random variables . ......................................................................................... 6 2. Continuous random variables . ................................................................................. 10 III. Sampling Distribution of Mean . .................................................................................... 10 A. An Example for Sampling Distribution . ..................................................................... 10 B. Process Going Into the Sampling Distribution Model . ............................................... 12 I. Refreshment: Relative Frequency Density and Probability Distribution A frequency distribution is a tabular summary of a set of data showing the frequency (or number) of items in each of several non- overlapping classes. Frequency Distribution 6 10 22 18 8 2 14 0 5 10 15 20 25 4 8 12 16 20 24 28 Grades Frequency frequency

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ECON 206 October 04, 2010 METU- Department of Economics Instructor: H. Ozan ERUYGUR e-mail: [email protected] 2 We can also graph relative frequency ( f/N ) using a bar graph, where f denotes frequency and N refers to the sum of all frequencies . Relative Frequency 0,075 0,125 0,175 0,275 0,225 0,1 0,025 0 0,05 0,1 0,15 0,2 0,25 0,3 4 8 12 16 20 24 28 Grades Relative Frequency relative frequency It is convenient to change the vertical scale to relative frequency density , which makes the total area (the sum of all the areas of the bars) equal to 1. o We can call this the probability distribution . Relative Frequency Density 0,01875 0,03125 0,04375 0,06875 0,025 0,00625 0,05625 0 0,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08 4 8 12 16 20 24 28 Grades Relative Frequency Density relative frequency/class width
ECON 206 October 04, 2010 METU- Department of Economics Instructor: H. Ozan ERUYGUR e-mail: [email protected] 3 / Relative Frequency Density= relative frequency f N class width class width = value class width frequency relative frequency relative frequency/class width 4 4 6 0,075 0,01875 8 4 10 0,125 0,03125 12 4 14 0,175 0,04375 16 4 22 0,275 0,06875 20 4 18 0,225 0,05625 24 4 8 0,1 0,025 28 4 2 0,025 0,00625 1 The histogram can now be used to find other experimental probabilities . Suppose we select a student from the class randomly. What would be the probability that this student has a grade between 12 and 20?

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ODTU 206 - ECON 206 METU Department of Economics LECTURE 01...

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