Consider the following probability distribution: align=center> a. Calculate for this distribution. b. Find the sampling distribution

Question:

Consider the following probability distribution:
align="center">

a. Calculate µ for this distribution.
b.
Find the sampling distribution of the sample mean for a random sample of n = 3 measurements from this distribution, and show that x is an unbiased estimator of µ.
c. Find the sampling distribution of the sample median m for a random sample of n = 3 measurements from this distribution, and show that the median is a biased estimator of µ.
d. If you wanted to use a sample of three measurements from this population to estimate µ, which estimator would you use? Why?

Distribution
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