L9-S2-CRV - PDF and Probability of Interval.pdf - Continuous Probability Distributions \u2013 Introduction and PDF Road Map Key Concepts \u2022 Definition and

L9-S2-CRV - PDF and Probability of Interval.pdf -...

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Continuous Probability Distributions – Introduction and PDF
Road Map Key Concepts Definition and Properties of the PDF Readings Associated Chapter 7 (7.1, 7.2)
Property 1 of the PDF 1. The PDF evaluated at any value of the random variable is non-negative: 𝑓𝑓 𝑥𝑥 0
Probabilities of intervals Recall that, for a discrete random variable, the probability of the interval [ 𝑎𝑎 , 𝑏𝑏 ] is the sum of all the probabilities of x within that interval. Example: For the binomial distribution with 6 trials the probability that the number of success is between 2 and 4 is 𝑃𝑃 2 ≤ 𝑥𝑥 ≤ 4 = 𝑝𝑝 2 + 𝑝𝑝 3 + 𝑝𝑝 4 = 𝑖𝑖=2 4 𝑝𝑝 ( 𝑥𝑥 𝑖𝑖 ) However, 𝑝𝑝 ( 𝑥𝑥 ) = 0 for continuous random variables. What do we do?
Probabilities of intervals

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• Fall '17
• Sheila Mammen

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