Math 203_Lecture 5

Math 203_Lecture 5 - Principles of Statistics 1 Lecture 5...

Info icon This preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
Principles of Statistics 1 Lecture 5: Math 203 Abbas Khalili Department of Mathematics and Statistics McGill University May 09, 2011 Principles of Statistics 1 Lecture 5: Math 203 – p. 1/4
Image of page 1

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

View Full Document Right Arrow Icon
Review of two concepts Independence and mutually exclusive Principles of Statistics 1 Lecture 5: Math 203 – p. 2/4
Image of page 2
Review of two concepts Independence and mutually exclusive Two events A and B are independent if P ( A | B ) = P ( B ) or P ( B | A ) = P ( B ) or equivalently P ( A B ) = P ( A ) P ( B ) Principles of Statistics 1 Lecture 5: Math 203 – p. 2/4
Image of page 3

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

View Full Document Right Arrow Icon
Review of two concepts Independence and mutually exclusive Two events A and B are independent if P ( A | B ) = P ( B ) or P ( B | A ) = P ( B ) or equivalently P ( A B ) = P ( A ) P ( B ) Two events A and B are mutually exclusive if A B = Principles of Statistics 1 Lecture 5: Math 203 – p. 2/4
Image of page 4
Review of two concepts Independence and mutually exclusive Two events A and B are independent if P ( A | B ) = P ( B ) or P ( B | A ) = P ( B ) or equivalently P ( A B ) = P ( A ) P ( B ) Two events A and B are mutually exclusive if A B = which implies P ( A B ) = 0 , and thus P ( A | B ) = 0 and P ( B | A ) = 0 . Principles of Statistics 1 Lecture 5: Math 203 – p. 2/4
Image of page 5

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

View Full Document Right Arrow Icon
If A and B are mutually exclusive, then P ( A B ) = P ( A ) + P ( B ) . Principles of Statistics 1 Lecture 5: Math 203 – p. 3/4
Image of page 6
Independence and mutually exclusive In general, the two concepts do not imply each other: Independence notarrowright mutually exclusive notarrowleft Principles of Statistics 1 Lecture 5: Math 203 – p. 4/4
Image of page 7

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

View Full Document Right Arrow Icon
Independence and mutually exclusive In general, the two concepts do not imply each other: Independence notarrowright mutually exclusive notarrowleft EXAMPLE : the experiment is rolling a six-sided fair die. A = { observing an odd number } B = { observing an even number } . Principles of Statistics 1 Lecture 5: Math 203 – p. 4/4
Image of page 8
Independence and mutually exclusive In general, the two concepts do not imply each other: Independence notarrowright mutually exclusive notarrowleft EXAMPLE : the experiment is rolling a six-sided fair die. A = { observing an odd number } B = { observing an even number } . Then A = { 1 , 3 , 5 } , B = { 2 , 4 , 6 } A B = . Principles of Statistics 1 Lecture 5: Math 203 – p. 4/4
Image of page 9

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

View Full Document Right Arrow Icon
Independence and mutually exclusive In general, the two concepts do not imply each other: Independence notarrowright mutually exclusive notarrowleft EXAMPLE : the experiment is rolling a six-sided fair die. A = { observing an odd number } B = { observing an even number } . Then A = { 1 , 3 , 5 } , B = { 2 , 4 , 6 } A B = . A and B are mutually exclusive. But not independent: P ( A ) = 3 6 , P ( B ) = 3 6 P ( A B ) negationslash = P ( A ) P ( B ) Principles of Statistics 1 Lecture 5: Math 203 – p. 4/4
Image of page 10
Example A stockbroker is researching 4 independent stocks. An investment in each stock will either make money or lose money. The probability that each stock will make money is 5/8 . Principles of Statistics 1 Lecture 5: Math 203 – p. 5/4
Image of page 11

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

View Full Document Right Arrow Icon
Example A stockbroker is researching 4 independent stocks. An investment in each stock will either make money or lose money. The probability that each stock will make money is 5/8 .
Image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern