If X1 and X2 are independent random variables with distribution given by P X;= -1] =P [X; = 1]=1/2 for i=1, 2, then are X1 and X¡ X2 independent?
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.
Xi is X1 and X2 for i=1,2 respectively. P[Xi=-1] denotes probability at X1=-1 and X2=-1 respectively. similarly,for P[Xi=1] denotes probability at X1=1 and X2=1. and we have to prove that X1 and X2 are independent.
![12.. If X1 and X2 are independent random variables with distribution given by P
[X;= -1]=P [X¡ = 1] =1/2 for i=1, 2, then are X, and X1 X2 independent?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5c185ae-c9c8-446b-ac28-0728574db119%2F6b80083d-e963-4969-be93-73d7f881ac46%2Fh6jehy_processed.png&w=3840&q=75)
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