Consider the population described by the probability distribution below. (25 points) x 3 5 7 P(x) 0.1 0.7 0.2 a. Find μ and sigma square. b. Find the sampling distribution of the sample mean x for a random sample of n = 2 measurements from the distribution. Show that x is an unbiased estimator of μ. c. Find the sampling distribution of the sample variance s2 for a random sample of n = 2 measurements from the distribution. Show that s2 is an unbiased estimator of sigma square.
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5) Consider the population described by the probability distribution below. (30 points)X357P(x)0.10.70.2a. Find µ and sigma square.μ = 3(0.1) * 5(0.7) * 7(0.2) = 5.2 (3 - 5.2)² (0.1) + (5 – 5.2)² (0.7) + (7 – 5.2)² (0.2) = 1.16b. Find the sampling distribution of the sample mean x for a random sample of n = 2 measurements from the distribution. Show that x is an unbiased estimator of μ.c. Find the sampling distribution of the sample variance s2 for a random sample of n = 2measurementsfrom the distribution. Show that s2 is an unbiased estimator of sigma square.
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