statistics Inductive Stats Random Sampling Unbiased Estimator

1. STATISTIC ASSIGNMENT – 1
- ADITYA JHUNJHUNWALA, 17001
Q1. WHAT IS INDUCTIVE STATISTICS?
Inductive statistics is the phase of statistics , which is concerned with the conditions under which conclusions
about populations can be drawn from analysis of particular samples.
The inferences drawn by inductive statistics are generally couched in the language of probability theory.
Inductive statistics is also known as inferential statistics.
Q2. DIFFERENCE BETRWWENPARAMETERAND STATISTICS?
The difference between a statistic and a parameter is that statistics describe a sample. A parameter describes an
entire population.
The ultimate goal of the field of statistics is to estimate a population parameter by use of sample statistics.
Parameters that we cannot measure directly. Statistics are the basis for all of statistical inference, since to infer
is to draw conclusions about a population from a sample.
Example - Suppose we study the population of dogs in Kansas City. A parameter of this population would be
the mean height of all dogs in the city. A statistic would be the mean height of 50 of these dogs.
Q3. WHAT IS RAMDOM SAMPLING?
Everyone in the entire target population has an equal chance of being selected.
This is similar to the national lottery. If the “population” is everyone who has bought a lottery ticket, then each
person has an equal chance of winning the lottery (assuming they all have one ticket each).
Random samples require a way of naming or numbering the target population and then using some type of raffle
method to choose those to make up the sample. Random samples are the best method of selecting your sample
from the population of interest.
The advantages are that your sample should represent the target population and eliminate sampling bias, but
the disadvantage is that it is very difficult to achieve
Q4. WHAT IS UNBIASED ESTIMATOR?EXAMPLE
An estimator is said to be unbiased if its bias is equal to zero for all values of parameter θ. A statistic is said to
be an unbiased estimate of a given parameter when the mean of the sampling distribution of that statistic can be
shown to be equal to the parameter being estimated.
For example, the mean of a sample is an unbiased estimate of the mean of the population from which the sample
was drawn.

2. Q5. WHAT IS BIASED ESTIMATOR?EXAMPLE
If an estimator is not an unbiased estimator, then it is a biased estimator.
A statistics t is said to be an biased estimator of a parameter if the expected value of t is θ,
Q6. WHAT IS MVUE? WHY IT IS CALLED THE BEST ESTIMATOR?
In statistics, a minimum-variance unbiased estimator (MVUE) is an unbiased estimator that has lower variance
than any other unbiased estimator for all possible values does of the parameter.
The estimator described above is called Minimum Variance Unbiased Estimator (MVUE) since, the estimates
are unbiased as well as they have minimum variance. Sometimes there may not exist any MVUE for a given
scenario or set of data. This can happen in two ways
1) No existence of unbiased estimators
2) Even if we have unbiased estimator, none of them gives uniform minimum variance.