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Exercise 3- Consider an exponentially distributed random variable f(X-.pdf

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Exercise 3. Consider an exponentially distributed random variable f ( X ; ) = exp ( x ) . (a) Show that the expected value of X is 1 . (b) Verify that the estimator ^ = 1/ x is biased, with bias equal to n 1 . Hint: you may use the fact that E [ i = 1 n x i 1 ] = n 1 . What happens as n ?.

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Exercise 3. Consider an exponentially distributed random variable f ( X ; ) = exp ( x ) . (a) Show that the expected value of X is 1 . (b) Verify that the estimator ^ = 1/ x is biased, with bias equal to n 1 . Hint: you may use the fact that E [ i = 1 n x i 1 ] = n 1 . What happens as n ?

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  • 1. Exercise 3. Consider an exponentially distributed random variable f ( X ; ) = exp ( x ) . (a) Show that the expected value of X is 1 . (b) Verify that the estimator ^ = 1/ x is biased, with bias equal to n 1 . Hint: you may use the fact that E [ i = 1 n x i 1 ] = n 1 . What happens as n ?