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Finding the Expected Value of the Largest Random Point from a Uniform Distribution

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Suppose 10 independent and random points are selected from a uniform distribution on the interval (0, 1). Let X denote the largest value of the 10 points. Find the expected value of X, E(X). (10) Hint: F(x) = P(X ? x) = P (all ten points ? x). Solution uniform distribution is given by f(x) = 1/(b-a) a<=x<=b E(X) = (a + b)/2 a = 0 b = 1 Therefore, E(X) = 1/2.

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Suppose 10 independent and random points are selected from a uniform distribution on the interval (0, 1). Let X denote the largest value of the 10 points. Find the expected value of X, E(X). (10) Hint: F(x) = P(X ? x) = P (all ten points ? x). Solution uniform distribution is given by f(x) = 1/(b-a) a<=x<=b E(X) = (a + b)/2 a = 0 b = 1 Therefore, E(X) = 1/2

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Finding the Expected Value of the Largest Random Point from a Uniform Distribution

  • 1. Suppose 10 independent and random points are selected from a uniform distribution on the interval (0, 1). Let X denote the largest value of the 10 points. Find the expected value of X, E(X). (10) Hint: F(x) = P(X ? x) = P (all ten points ? x). Solution uniform distribution is given by f(x) = 1/(b-a) a<=x<=b E(X) = (a + b)/2 a = 0 b = 1 Therefore, E(X) = 1/2