Let X(1),X(2),.....,X(n) be independent and identically distributed random variables each having mean u and standard deviation sigma^2 . Assume that we do not know the distribution of X(i) , n=1......n, Let Y = (X(1)+X(2)+....+X(n) ) / n Prove that the expected value of the random variable Y is u. the variance of the random variable Y is sigma^2 / n What can be said about the distribution of Y when n is large
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Let X(1),X(2),.....,X(n) be independent and identically distributed random variables each having mean u and standard deviation sigma^2 . Assume that we do not know the distribution of X(i) , n=1......n,
Let Y = (X(1)+X(2)+....+X(n) ) / n
Prove that
- the
expected value of the random variable Y is u. - the variance of the random variable Y is sigma^2 / n
- What can be said about the distribution of Y when n is large
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