Basics of Probability and Statistics Week 1 Challenge

Ans 1: A sample is used to calculate varience and standard deviation when data for complete population is not known. So the denominator(in the varience formula for sample) is divided by a number 1 less than the actual sample size to get a higher value of varience and standard deviation as compared to value calculated using complete population data,to compensate for lack of availability of complete population data.

Ans 2: In cluster sampling some natural trait or characteristics divides the population into samples or clusters and then one of the whole cluster is selected using simple random sampling techniques for calculation.

while in stratified sampling we have to use a strategy to divide a population into small groups or samples using some trait or characteristics. and then we pick potential candidate or quantity from each group to form actual sample.

example- a box full of different colour balls ,and we need to take sample using both techniques.

• In cluster sampling the balls are divide on the basis of colour and 6 different clusters or groups are formed and ultimately 1 cluster or sample is selected using simple random sampling for calculation.
• But in stratified sampling after dividing balls on the basis of colour, they are numbered and a particular number of balls are selected from each group using simple random sampling to form the actual sample.

Ans 3: case 1-Number of samples, if sample size is fixed ,for a population of size n is given by :-

n!/((n!)*(n-P)!) (where p is the sample size)

case 2- Number of samples ,if sample size is not fixed and sample size may vary between 1 to n-1 for a population size n

n + ∑ n!/(r!*(n-r)!) (where r goes from 2 to n-1)

Ans 4: probability of getting jack in 1st draw = 4/52

robability of getting jack in 2nd draw = 3/51

probability of getting 2 consecutive jack = (4/52)*(3/51) = 1/221

Ans 5: sample space for getting same number on the two dices are (1,1),(2,2),(3,3),(4,4),(5,5),(6,6)

so,possible outcomes = 6

total outcomes= 36

probability of getting same number on both dice = 6/36 =1/6

Ans 6: Varience is a intermediate term to measure dispersion, it changes the units of actual physical quantity which we are analysing,so we need to bring back the modified dispersion units to original units which is done by calculating standard deviation. which helps in actual analysis of variation of any physical quantity.