STAT211 Chapter 6: Chapter 6

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Chapter 6.1-6.5 (Continuous Random Variables)
Expectation for Continuous Random Variables: E(X) = u = ∫-xf(x)dx
Expectation for a Function: E(g(X)) = ∫-g(x)f(x)dx
Variance: E[(X-u)^2] = E(X^2) – [E(X)]^2
Continuous Normal Distribution: Probability is found by the area underneath the curve.
Probability with Integration Example:
Given f(x) = 3x2 for 2 < x < 4 what is P(X > 3)?
Ans: P(X>3) = 43 (3x2dx) = 3 43 (x2dx) = 3 [x3/3]4
3 = 3 * [43/3 – 33/3]
Continuous Uniform Distribution: Areas underneath the curve are rectangles, so no
integration is required.
u = (d + c)/2 = median o2 = 1/12(d – c)2
Standard Normal Distribution: A normal distribution with u = 0 and o = 1.
Z = (X – u)/o
X ~ N(u, o2)
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