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

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Background image of page 2
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?
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 12

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online