Basics of Probability and Statistics Week 1 Challenge

Answer 1:

The formula to calculate population variance is:

σ² = Σ (x_i – μ)² / N

The formula to calculate sample variance is:

s² = Σ (x_i – x)² / (n-1)

When calculating the sample variance, we apply Bessel’s correction, hence, dividing it by n-1.

This method corrects the bias in the estimation of the population variance.

Answer 2:

Difference betweem Clustered sampling & Stratified sampling :

Clustered sampling method is a sampling method in which we split a population into clusters, then randomly select some of the clusters and include all members from those clusters in the sample.

Stratified sampling is a sampling method in which we split a population into groups, then randomly select some members from each group to be in the sample.

Answer 3:

for the population size n = 2, samples which we can get are : {1},{2},{1,2},𝜙 (If we consider empty sample as well)

for population size n= 3, samples which we will get : {1},{2},{3},{1,2},{1,3},{2,3},{1,2,3},𝜙 (If we consider empty sample as well)

Hence, answer would be 2ⁿ

Answer 4:

In a deck of 52 cards, there are 4 jack cards. Hence, probability of drawing 2 jack cards will be:

Favourable outcome = C(4,2) = 6

Total Outcomes = C(52,2) = 1326

Hence answer = 6/1326 = `1/221`

Answer 5:

When rolling two dices, total possible outcomes are 6*6 = 36, and out of them 6 are favourable i.e (1,1),(2,2),(3,3),(4,4),(5,5),(6,6)

Hence answer = `6/36=1/6`

Answer 6:

Variance is required to compute the deviation of the values from mean , and it is required to square each deviation so that they don't cancel each other. Now, standard deviation is required for units and dimensioning in the same unit in which the values are in .