In: Statistics and Probability
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)?
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