Let X be a continuous random variable with probability density function 2x f(x; 0) = () e-²/0 for x > 0 (and zero otherwise), where 0 > 0 is an unknown parameter, and let X1, X2, ..., Xn be a random sample the distribution of X.
Let X be a continuous random variable with probability density function 2x f(x; 0) = () e-²/0 for x > 0 (and zero otherwise), where 0 > 0 is an unknown parameter, and let X1, X2, ..., Xn be a random sample the distribution of X.
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.CR: Chapter 13 Review
Problem 29CR
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Transcribed Image Text:Let X be a continuous random variable with probability density function
2x
-x²/0
f(x; 8) = (
for x > 0 (and zero otherwise),
where 0 > 0 is an unknown parameter, and let X1, X2, ...,Xn be a random sample from
the distribution of X.
Show that E(X²) = 0 and Var(X²) = 0².
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