Q3) a) What is Mean Squared error (MSE) of an estimator ô ? Show that MSE (Ô) = Variance (Ô ) + (Bias ( ))? b) Suppose that X denotes the mean of a random sample of size n from a normal population with mean u and variance of whereas Y denotes the mean of a random sample of size n from a normal population with mean u and variance ož .Let the estimator for µ be a = aX +(1-a)Y i) Show that A is an unbiased estimator of µ. ii) For what value of a would the variance of this estimator be a minimum? c) Let X be a continuous random variable that is uniformly distributed over (0, B). Find the moment estimator of ß.

Q3) a) What is Mean Squared error (MSE) of an estimator ô ? Show that MSE (Ô) = Variance (Ô ) + (Bias ( ))? b) Suppose that X denotes the mean of a random sample of size n from a normal population with mean u and variance of whereas Y denotes the mean of a random sample of size n from a normal population with mean u and variance ož .Let the estimator for µ be a = aX +(1-a)Y i) Show that A is an unbiased estimator of µ. ii) For what value of a would the variance of this estimator be a minimum? c) Let X be a continuous random variable that is uniformly distributed over (0, B). Find the moment estimator of ß.

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Description: Q3) a) What is Mean Squared error (MSE) of an estimator ô ?Show that MSE (Ô) = Variance (Ô ) + (Bias ( ))?b) Suppose that X denotes the mean of a random sample of size n from a normalpopulation with mean u and variance of whereas Y denotes the mean

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Question

Q3) a) What is Mean Squared error (MSE) of an estimator ô ?
Show that MSE (Ô) = Variance (Ô ) + (Bias ( ))?
b) Suppose that X denotes the mean of a random sample of size n from a normal
population with mean u and variance of whereas Y denotes the mean of a random sample
of size n from a normal population with mean u and variance ož .Let the estimator for µ
be a = aX +(1-a)Y
i) Show that A is an unbiased estimator of µ.
ii) For what value of a would the variance of this estimator be a minimum?
c) Let X be a continuous random variable that is uniformly distributed over (0, B). Find the
moment estimator of ß.

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