Topic 5 Overview - wiki

Topic 5 Overview - wiki - Topic 5 Overview Consider 2 or...

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Topic 5 Overview Consider 2 or more random variables. Joint PMF or PDF Expected value and variance Central Limit Theorem (CLT) What is Joint Distribution? Discrete Given 2 Bernoulli discrete random variables X and Y (not independent) Joint Probability Mass Function 1. 2. 3. Marginal PMF of X: (also satisfies 1 & 2) 4. Marginal PMF of Y: (also satisfies 1 & 2) Continuous Let X and Y be continuous random variables: Note that whatever comes first in is the outer integral Marginal Cases: Example Independence
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if discrete if continuous You should be able to factor joint PDF into two functions: x alone and y alone For example, if X and Y are independent, . Conditional Distributions If X and Y are continuous, the result of the above equation will be since Y is set to a certain constant number. The way to get around it is by looking at the joint PDF and marginal PDF: After finding symbolic conditional PDF, integrate over X and plug in Y Example Suppose X and Y denote the air pressure in the front tires
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