lecture6

lecture6 - Stat 302, Introduction to Probability Jiahua...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Stat 302, Introduction to Probability Jiahua Chen January-April 2011 Jiahua Chen () Lecture 6 January-April 2011 1 / 41 Average In a class of students, 30% of them get exactly 60, 50% of them get 80 and 20% of them get 95 in their final exam. What is the class average of this final exam? Apparently, the average is given by 0.30 60 + 0.50 80 + 0.20 95 = 77. Jiahua Chen () Lecture 6 January-April 2011 2 / 41 Average In a class of students, 30% of them get exactly 60, 50% of them get 80 and 20% of them get 95 in their final exam. What is the class average of this final exam? Apparently, the average is given by 0.30 60 + 0.50 80 + 0.20 95 = 77. Note that we did not use information on how many students this class has. Jiahua Chen () Lecture 6 January-April 2011 2 / 41 Average for a random variable In a class of students, 30% of them get exactly 60, 50% of them get 80 and 20% of them get 95 for their final marks. If I randomly select a student from this class, and let X be his/her final mark. What is the probability mass function of X ? Jiahua Chen () Lecture 6 January-April 2011 3 / 41 Average for a random variable In a class of students, 30% of them get exactly 60, 50% of them get 80 and 20% of them get 95 for their final marks. If I randomly select a student from this class, and let X be his/her final mark. What is the probability mass function of X ? The pmf of X is given by p ( 60 ) = 0.3; p ( 80 ) = 0.5; p ( 95 ) = 0.2. Jiahua Chen () Lecture 6 January-April 2011 3 / 41 Average for a random variable In a class of students, 30% of them get exactly 60, 50% of them get 80 and 20% of them get 95 for their final marks. If I randomly select a student from this class, and let X be his/her final mark. What is the probability mass function of X ? The pmf of X is given by p ( 60 ) = 0.3; p ( 80 ) = 0.5; p ( 95 ) = 0.2. In view of these information, what is the average mark of a randomly selected student? Jiahua Chen () Lecture 6 January-April 2011 3 / 41 Average for a random variable While the outcome of X is random due to the randomness in selecting the student, the proportion of times when X = 60 is clearly 30% if we have it repeated INFINITE many times. Similarly, 50% of such X values are 80, and 20% such values are 95. Thus, it is sensible to use the average outcomes over INFINITE repetitions as the average size of X . Let us tentatively define the Expectation of this X as E ( X ) = 0.30 60 + 0.50 80 + 0.20 95 = 77. Jiahua Chen () Lecture 6 January-April 2011 4 / 41 Average for a random variable Suppose X is a discrete random variable and its range is given by { x 1 , x 2 , . . . , } , and its pmf is given by p ( x ) . We define the expectation of X as E ( X ) = ?...
View Full Document

Page1 / 66

lecture6 - Stat 302, Introduction to Probability Jiahua...

This preview shows document pages 1 - 9. Sign up to view the full document.

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