A box contains 5 chips marked 1,2,3,4, and 5. One chip is drawn at random, the...

A box contains 5 chips marked 1,2,3,4, and 5. One chip is drawn at random, the number on it is noted, and the chip is replaced. The process is repeated with another chip. Let X1,X2, and X3 the outcomes of the three draws which can be viewed as a random sample of size 3 from a uniform distribution on integers.
a [10 points] What is population from which these random samples are drawn? Find the mean (µ) and variance of this population (σ2)?

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Expert Solution

A box contains 5 chips marked 1,2,3,4, and 5.

One chip is drawn at random, the number on it is noted, and the chip is replaced. The process is repeated with another chip.

Let X1,X2, and X3 the outcomes of the three draws which can be viewed as a random sample of size 3 from a uniform distribution on integers.

To calculate : 1) the population from which these random samples are drawn

2) the mean (µ) and

3) variance of this population σ²

Now,

Therefore 1) the population from which the random sample are drawn is 1/5.

2) mean, µ = 3 and

3) population variance, σ² = 2

orchestra answered 2 years ago

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