Basics of Probability and Statistics Week 1 Challenge

1ans.

The formula for sample variance is different from population variance because they are based on different sets of data. Two Quantities that we are considering here . The reason behind the Denominator being (n-1) , is that the total degrees of freedom of this sample system with n samples is n-1 .

2 ans.

In Cluster Sampling, the sampling is done on a population of clusters therefore, cluster/group is considered a sampling unit. In Stratified Sampling, elements within each stratum are sampled. In Cluster Sampling, only selected clusters are sampled. In Stratified Sampling, from each stratum, a random sample is selected.

3ans.

The number of different samples of size n that can be selected from a finite population of size N is given by the combination formula, which is denoted as NCn. This formula is defined as NCn=N!.

4ans.

two cards can be drawn from a pack of 52 playing cards 52C2 ways,

52*51\2. the probablility of getting 2 jacks is 4c2 6 ways

6/1326 = 1/221.

5ans

probability of getting same number on both? Sample points of getting same number on both dice- (1,1) ,(2,2) ,(3,3) ,(4,4) ,(5,5) & (6,6). Hence, the probability of getting same number on both the dice is 1/6.

6ans.

The reason why standard deviation is so popular as a measure of dispersion is its relation with the normal distribution which describes many natural phenomena and whose mathematical properties are interesting in the case of large data sets