Suppose and are real-valued random variables with as their common probability density function, and is a sample generated by them. The expectation of the number of observations in the sample that fall within a specified interval is
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Suppose X₁ and X₂ are real-valued random variables with f as their common probability density function, and (x₁,x₂) is a sample generated by them. The expectation of the number of observations in the sample that fall within a specified interval [a,b] is (A) (∫ₐ^bf(x) dx)² (B) ∫ₐ^bx²f(x) dx (C) 2∫ₐ^bf(x) dx (D) ∫ₐ^bxf(x) dx
Also written as: Suppose X_1 and X_2 are real-valued random variables with f as their common probability density function, and (x_1,x_2) is a sample generated by them. The expectation of the number of observations in the sample that fall within a specified interval [a,b] is
Probability and Bayes' theorem has come up 190 times in 7 exams since 2004.
This question is on Expectation by indicator variables, part of Probability and Bayes' theorem in Statistics.
Finding expected counts by adding up simple 0-1 variables.
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Question from the DSE 2010 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.