Basics of Probability and Statistics Week 1 Challenge

Question 1:

Most of the time we do not know µ and we estimate it with x. The formula for S^2 measures the squared deviations from x rather than µ . The xi’s tend to be closer to their average x rather than µ , so we compensate for this by using the divisor (n-1) rather than n.

Question 2:

In Stratified Sampling, the population is separated into different homogeneous segments called ‘strata’, and then the sample is chosen from the each stratum randomly

In Cluster Sampling, the units of the population are randomly selected from already existing groups called ‘cluster.’

In stratified sampling, there is homogeneity within the group, whereas in the case of cluster sampling the homogeneity is found between groups.

Question 3:

From population of size n, anywhere between 1 to n number of samples can be created. But it is advised that a good maximum sample size is usualy 10% as long as it does not exceed 1000.

Question 4:

Answer: 1/221

Explanation:

for first jack: 1(in four jacks) from 52(cards in a deck) => 4/52

For Second Jack : 1 (in remaining 3 jacks) from 51(remaining cards in the deck) => 3/51

(The chance of drawing the first card) X (The chance of drawing the second card) => (4/52)*(3/51) => 1/221

Question 5:

Answer : 1/6

Explanation: For first dice roll : probability of any number appiarence = 6/6 => 1

For the Sencond roll: probablity of appiaring the same number as first roll outcome = 1/6

Probability of both these events to happen = 1*(1/6) = 1/6

Question 6:

Yes variance can measure the dispersion in data, But the varience value is not compatible with any standard metric. since we had to square the standard metric value in order to find the varience, We need to have that value square rooted to make that value compatible with the standard metric.

**Week 1 Challenge complete**

Thank you!!