probability

1. MATHEMATICS IV: MA202
LECTURE 7

2. JOINT RANDOM VARIABLES|EXAMPLE
• The response time is the speed of page
downloads and it is critical for a mobile Web
site.
• As the response time increases, customers
become more frustrated and potentially
abandon the site for a competitive one.
• Let X denote the number of bars of service on
the mobile device.
• Let Y denote the response time (to the nearest
second) for a particular user and site.

3. JOINT PROBABILITY MASS FUNCTION
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4. JOINT PROBABILITY DENSITY FUNCTION
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5. EXAMPLE |SERVER ACCESS TIME
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6. MARGINAL PROBABILITY DISTRIBUTION |
EXAMPLE
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7. MARGINAL PROBABILITY DENSITY FUNCTION
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8. MARGINAL PROBABILITY DENSITY FUNCTION|
EXAMPLE SERVER ACCESS TIME
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9. CONDITIONAL PROBABILITY
DISTRIBUTION |EXAMPLE
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10. CONDITIONAL PROBABILITY DENSITY
FUNCTION
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11. CONDITIONAL PROBABILITY| EXAMPLE
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12. CONDITIONAL MEAN AND VARIANCE |
EXAMPLE
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13. INDEPENDENCE
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14. INDEPENDENCE EXAMPLE
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15. COVARIANCE
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When two or more random variables are defined on a
probability space, it is useful to describe how they vary
together.

16. COVARIANCE
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17. COVARIANCE
Zero Covariance does not imply independence!

18. CORRELATION
There is another measure of the relationship
between two random variables that is usually
easier to interpret than covariance.
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