Consider the population described by the probability distribution below. Find mu

Question

Consider the population described by the probability distribution below. Find mu. Find the sampling distribution of the sample mean for a random sample of n = 3 measurements from this distribution. Find the sampling distribution of the sample median for a random sample of n = 3 observations from this population. Show that both the mean and the median are unbiased estimators of mu for this population. Find the variances of the sampling distributions of the sample mean and the sample median. Which estimator would you use to estimate mu? Why?

Explanation / Answer

a)

mean = x * P(x)

= 0 * 1/3 + 2 * 1/3 + 4 * 1/3

= 2

std. deviation = ( (x)^2 * p(x) - 9mean)^2)

= ((0)^2 * 1/3 - (2) ^2 + ( 2)^2 * 1/3 -( 2)^2 + (4)^2 * 1/3 - (2)^2)

= -5.33

b) sampling distribution of sample mean = mean of the population

= 2

c) Sample median = 1.253 * sigma / sqrt(n)

= 1.253 * -5.33 / sqrt(3)

= -3.85

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.