BEGINNER STAT QUESTION! NEED HELP ASAP! Please be thorough with each part :) 2.
ID: 3305654 • Letter: B
Question
BEGINNER STAT QUESTION! NEED HELP ASAP! Please be thorough with each part :)
2. This problem will lead you through the steps of determining the probability distribution, mean, and variance of the random variable ï, the sample mean. Consider the population made up of only three individuals with corresponding values 1. 2, and 4. The specific sampling procedure vou will use involves randomly selecting a sample of size n - 2 from the population with replacement. Sampling with replacement means that each time an individual is drawn from the population, its value is recorded and then the individual is returned to the pool of individuals available selection on the next draw (a) First, consider the scenario where a single individual is selected from the population at random. Define the random variable X as the observed value of the one selected individual. Write out the possible values of X and their associated probabilities in the form of probability distribution table. Then calculate the mean, ux, and standard deviation, (b) Now, consider the scenario described above where a sample of n 2 individuals is randomly selected from the population with replacement. Write out each of the possible outcomes of the sampling procedure by writing out each pair of observed values that could result when you draw the random sample. (There are nine possible outcomes of the form (xi,x2).) (c) Define the random variable z as the mean value of the two individuals randomly selected from the population. Write out the possible values of c and their associated probabilities in the form of probability distribution table. (There are six possible values of x.) Then calculate the mean, Hz, and standard deviation, oz. (d) Verify that As-Ax and Ox/v/n are true statements in this context.Explanation / Answer
mean are eqaul im both case = 2.333
sd(Xbar) = sd(X) /sqrt(n)
as 1.08123 = 1.527525 /sqrt(2)
x p xp x^2p 1 0.333333 0.333333 0.333333 2 0.333333 0.666667 1.333333 4 0.333333 1.333333 5.333333 mean 2.333333 sd 1.527525 x1 x2 p xbar xbar p xbar*p 1 1 0.111111 1 1 0.111111 0.111111 1 2 0.111111 1.5 1.5 0.222222 0.333333 1 4 0.111111 2.5 2 0.111111 0.222222 2 1 0.111111 1.5 2.5 0.222222 0.555556 2 2 0.111111 2 3 0.222222 0.666667 2 4 0.111111 3 4 0.111111 0.444444 4 1 0.111111 2.5 4 2 0.111111 3 mean 2.333333 4 4 0.111111 4 sd 1.080123Related Questions
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