On a Mother Population, we get a set of occurrences 18; 10; 2; 1; 5; 9 Question.1) random variable M on this Mother Population What does set E represent for M? Describe the population, justify your choice Then, give the distribution of random variable M and justify your choice
Formula +Proof+ Computation of the Expected value of M Formula +Proof+ Computation of the variance of M Formula + Computation of the standard deviation of M
Question.2) SAMPLES: Write the construction and properties of any sample of size n. Then give the construction of any random vector-sampling for samples of size 2-justify.
How many different sample of size n can we get from k elements of E? Then: How many different sample of size n=2 can we get from those elements of
Question.3) DISTRIBUTION of the EMPIRICAL MEAN
Write the definition and expression (way of computation) of the empirical mean (general formula) What does the Empirical Mean represent?
Construction (justify it) of the table of values of the empirical mean
Deduce from it, and justify the computations, le distribution table of the empirical mean
Formula + Computation of the Expected value of the empirical mean:
• Method 1: Computation (direct) from the distribution table
• Method 2: With the general result for the empirical mean, justify the result (use M also)
Formula + Computation of the variance of the empirical mean:
• Method 1: Computation (direct) from the distribution table
• Method 2: With the general result for the empirical mean, justify the result (use M also)
Formula + Computation of the standard deviation of the empirical mean