Question

Explain Central Limit Theorem.     

What is the sampling distribution of the mean?

Explain the differences between a discrete random variable and a continuous random variable.      

Answer 1

a) Central limit theorem:

   Let X1,X2...Xn be the random sample with     and   > o . Then the probability distribution of

          or    for lage n

Importance:

   When we have large sample with mean and standard deviation, but known probability distribution. Then for large sample size ,we can use central limit theorem as approximation. Once we know the the probability distribution then its easy to analyse data.

            Therefore it is mostly used for large sample,

b) What is the sampling distribution of the mean?
Ans:

what is the sampling distribution of the mean, the overall mean, and the standard error of the mean?

sampling distribution of the mean will be xbar

standard error of the mean will be SD / srqt (n)
Is a normal distribution an approproate assumption for the sampling distribution of the mean?

if n > 30 then yes is a normal distribution

c) Explain the differences between a discrete random variable and a continuous random variable.      

Discrete random variable: random variablesthat can assume a countable number of values are calleddiscrete.

For example: the number of voters ina sample of 1000 who favor impeachment of the president: x= 0, 1, 2,........,1000

Continuous random Variable: random variables that canassume values corresponding to any of the points contained in aninterval are called continuous.

For example: the depth (in feet) atwhich a successful oil-drilling venture first strikes oil:, where c is the maximum depthobtainable.

Note that several of the examples of discrete random variablesbegin with the words The numberof......... This wording is very common, since thediscrete random variables most frequently abserved arecounts.