Basics of Probability and Statistics Week 1 Challenge

1. Ans: The difference between variance and sample variance relates to calculation of variance. If a variance in the sample is calculated we are neglecting the lack of information regarding the population size. So the sampe variance will definitly be greater than the variance of the population size. To compensate for this difference we are introducing the n-1 in denominator for sample while it is n for population.

2.Ans:

Clustered Sampling	Stratified sampling
Cost reduction method	Better precision
Heterogenous groups	Homogenous groups
Randomly selected clusters as groups	Randomly selected members from strata
More errors	Less errors

3.Ans For any population of size N the number of sampleas size is (n^3-1).

4. the no of cards in a deck = 52

the number of jacks in a deck = 4

the probability of drawing a first jack = 4/52

After drawing the first jack the probablility of drawing a second jack = 3/51

The total = (4/52) * (3/51) = 12/2652

5.The total no of possibilities for 2 dices = 36

The total no of doubles possibilities = 6

The Total possibility of getting a double = 6/36 = 1/6

6. The variance is calculated by taking the X-mean which could have negative values so we take (x-mean)^2 to make it a positive integer. So later when we calculate the variance it is the square of the standard deviation. Hence we take square root of variance to get the standard deviation