Basics of Probability and Statistics Week 1 Challenge

Population vs. Sample Variance:

• Population: Divide by $N$N.
• Sample: Divide by $n-1$n−1 to reduce bias (Bessel's correction).

Stratified vs. Clustered Sampling:

• Stratified: Divide population into groups, then sample from each group.
• Cluster: Divide population into groups, then sample whole groups.

Number of Samples from Population of Size $n$n:

• Without a specified size: $2^n$2n possible subsets.

Probability of Drawing 2 Jacks:

• $\frac{4}{52} \times \frac{3}{51} = \frac{1}{221} \approx 0.0045$524​×513​=2211​≈0.0045.

Probability of Same Numbers on 2 Dice:

• $6/36 = 1/6 \approx 0.167$6/36=1/6≈0.167.

Why Standard Deviation Over Variance:

• Standard deviation is in the same unit as the data, making it more interpretable.