SOLUTION: Consider a population consisting of 5 elements: {1,2,3,4,5}. We will draw a sample of size two from this population and calculate the average of drawn numbers. For example, we ca

Question 1177077: Consider a population consisting of 5 elements: {1,2,3,4,5}. We will draw a sample of size two from this population and calculate the average of drawn numbers. For example, we can get numbers 1 and 5, the average is then 3 or numbers 3 and 4, their average is 3.5. The averages with their probabilities are probability distribution. It is an example of a sampling distribution with sample size 2.
How many different samples (without replacement) we have in this case?
How many different values does the random variable x̄ assume?
What is the probability of getting average 5?

What is the probability of getting average 2.5?

(write your answer as a fraction a/b or as an integer)
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

How many different samples (without replacement) do we have in this case?

ANSWER: "5 choose 2" = (5*4)/(2*1) = 20/2 = 10

How many different values does the random variable x̄ assume?

To this point in your post you have not specifically that x-bar is the average. But since you talk about the average later in your post, and since using x-bar for an average is standard, I will assume that is what it is.

The smallest possible sum is 1+2=3 and the largest is 4+5=9, and clearly all the whole number sums between 3 and 9 can be obtained. That make seven different values for the sum; and that of course means seven different values for the average.
ANSWER: 7

What is the probability of getting average 5?

The largest sum we can get is 9; the largest average we can get is 4.5.

ANSWER: P(x-bar=5) = 0

What is the probability of getting average 2.5?
An average of 2.5 means a sum of 5. There are 2 ways to get a sum of 5 -- 1 and 4, or 2 and 3. Since there are 10 different samples possible....

ANSWER: P(x-bar=2.5) = 2/10 = 1/5

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