Basics of Probability and Statistics Week 1 Challenge

1. The denominator of variance of population is different from that of sample because, n-1 samples are in-dependent but the last element is determined on its own and it is not free to change. This is done to get the best estimate of population mean from the sample mean.

2. In stratified sampling, we group items based on their categories and select the required number of samples randomly from each group.

In clustered sampling, we make different clusters, where each cluster contain the items with very similar features, based on the clusters we sample only selected clusters according to our requirement.

3. We can determine the number of samples to be created by using,`((z_{alpha/2} sigma)/E)^2`

where

`z_{alpha/2}` is the critical value,

`sigma` is the standard deviation of population

`E` is the maximum difference between the observed sample mean and the population mean .

4.

Probability of picking 1st Jack = `4/52`

Probability of picking 2nd Jack = `3/51`

Hence probability of picking 2 jacks =

`4/52*3/51=12/2652` = `1/221`

5. For getting the same number on both die, there will be 6 possibilities which are (1,1),(2,2),(3,3),(4,4),(5,5) and (6,6). Hence, the required probability is 6/36 = 1/6.

6. Because we square the values and units while calculating the variance and hence to bring back the units back to their original form it is necessary to calculate the standard deviation.