Let X, X, ... , X, be a random sample from a population that is uniformly distributed over (a, b), a, b e R, a < b. Let x be the sample mean and Y, = min {X, : i = 1, . .., n}. • Using chebyshev's inequality, show that & converges to (b-a)/2 in probability

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 54E
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Let X,, X2, ..., X, be a random sample from a population that is uniformly distributed
over (a, b), a, b e R, a < b. Let x be the sample mean and Y, = min {X; : i = 1, ..., n}.
• Using chebyshev's inequality, show that x converges to (b-a)/2 in probability
Transcribed Image Text:Let X,, X2, ..., X, be a random sample from a population that is uniformly distributed over (a, b), a, b e R, a < b. Let x be the sample mean and Y, = min {X; : i = 1, ..., n}. • Using chebyshev's inequality, show that x converges to (b-a)/2 in probability
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