Basics of Probability and Statistics Week 1 Challenge

1. σ² = Σ (x_i – μ)² / N

2.

• In stratified sampling, a sample is drawn from each strata (using a random sampling method like simple random sampling or systamatic sampling ). In the image below, let’s say you need a sample size of 6. Two members from each group (yellow, red, and blue) are selected randomly. Make sure to sample proportionally: In this simple example, 1/3 of each group (2/6 yellow, 2/6 red and 2/6 blue) has been sampled. If you have one group that’s a different size, make sure to adjust your proportions. For example, if you had 9 yellow, 3 red and 3 blue, a 5-item sample would consist of 3/9 yellow (i.e. one third), 1/3 red and 1/3 blue.
• In cluster sampling,the sampling unit is the whole cluster; Instead of sampling individuals from within each group, a researcher will study whole clusters. In the image below, the strata are natural groupings by head color (yellow, red, blue). A sample size of 6 is needed, so two of the complete strata are selected randomly (in this example, groups 2 and 4 are chosen).

3.

Number of possibilities while tossing a coin = 2

Number of possibilities while tossing 3 coins together = 2³

= 8

Sample Space :

{ (H,H,H) , (H,H,T) , (H,T,H) , (H,T,T) ,

(T,H,H) , (T,H,T) , (T,T,H) , (T,T,T) }

6 sample points are having head and tail both.

P(E) = 6/8

= 3/4

Total number of outcomes = 8

Sample Space :

{(H,H,H) , (H,H,T) , (H,T,H) , (H,T,T) ,

(T,H,H) , (T,H,T) , (T,T,H) , (T,T,T)}

Number of favourable outcomes = 4

Probability = 4/8

= 1/2

5.

Finding Variance:

Variance =

Here, n=8