Let X1, ..., Xn be independent uniform rvs on the interval (0, 1). a. What are the mean u and the sd o of a uniform rv on the interval (0, 1)? X-u b. How large does n need to be before the pdf of is approximately that of a standard normal rv? (Nete: there is no fright" answer as it onondo by fappreximotoly " Vou should try

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 28E
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Let X1,..., Xn be independent uniform rvs on the interval (0, 1).
a. What are the mean u and the sd o of a uniform rv on the interval (0, 1)?
b. How large does n need to be before the pdf of is approximately that of a standard normal rv?
(Note: there is no “right" answer, as it depends on what is meant by "approximately." You should try
various values of n until you find the lowest one where the estimate of the X distribution is still close to
standard normal.)
Transcribed Image Text:Let X1,..., Xn be independent uniform rvs on the interval (0, 1). a. What are the mean u and the sd o of a uniform rv on the interval (0, 1)? b. How large does n need to be before the pdf of is approximately that of a standard normal rv? (Note: there is no “right" answer, as it depends on what is meant by "approximately." You should try various values of n until you find the lowest one where the estimate of the X distribution is still close to standard normal.)
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