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The product of a binomial, which has the form ( (a + b) ), and a special multinomial, such as ( (x + y + z)^n ), is obtained by distributing the binomial across the multinomial. This results in each term of the multinomial being multiplied by each term of the binomial, leading to a new expression that combines all possible products. For example, multiplying ( (a + b) ) by ( (x + y + z)^n ) involves distributing ( a ) and ( b ) across each term of the multinomial, effectively creating a new polynomial that includes terms of the form ( a \cdot (x + y + z)^n ) and ( b \cdot (x + y + z)^n ). The result is a polynomial that retains the combinatorial structure of the multinomial.
Lulla diference
No. It is multinomial because you have more than two possible outcomes each time.
multiterm mathematical expression: a mathematical expression consisting of the sum of a number of terms, each of which contains a constant and variables raised to a positive integral power
There are many frequency distributions: Uniform, Binomial, Multinomial, Poisson, Gaussian, Chi-square, Student's t, Fisher's F, Beta, Gamma, Lognormal, Logistic to name some off the top of my head. And I am sure I've missed many more. You need to specify which ones you are interested in. Forgot the Exponential.
multinomial
True.
The special products include: difference of the two same terms square of a binomial cube of a binomial square of a multinomial (a+b) (a^2-ab+b^2) (a-b) (a^2+ab+b^2)
The product of a binomial, which has the form ( (a + b) ), and a special multinomial, such as ( (x + y + z)^n ), is obtained by distributing the binomial across the multinomial. This results in each term of the multinomial being multiplied by each term of the binomial, leading to a new expression that combines all possible products. For example, multiplying ( (a + b) ) by ( (x + y + z)^n ) involves distributing ( a ) and ( b ) across each term of the multinomial, effectively creating a new polynomial that includes terms of the form ( a \cdot (x + y + z)^n ) and ( b \cdot (x + y + z)^n ). The result is a polynomial that retains the combinatorial structure of the multinomial.
The special products include: difference of the two same terms square of a binomial cube of a binomial square of a multinomial (a+b) (a^2-ab+b^2) (a-b) (a^2+ab+b^2)
Lulla diference
No. It is multinomial because you have more than two possible outcomes each time.
multiterm mathematical expression: a mathematical expression consisting of the sum of a number of terms, each of which contains a constant and variables raised to a positive integral power
There are many frequency distributions: Uniform, Binomial, Multinomial, Poisson, Gaussian, Chi-square, Student's t, Fisher's F, Beta, Gamma, Lognormal, Logistic to name some off the top of my head. And I am sure I've missed many more. You need to specify which ones you are interested in. Forgot the Exponential.
No. If you keep track of all the numbers that are rolled then there are six possible outcomes, a binomial has only two. It is a multinomial distribution.
Monomial consisting of one term ( 3x ) , Binomial consisting of two terms ( x + y ), Trinomial consisting of three terms ( 3x+4x+5xy ), and Multinomial consisting of three or more terms.
It is just a factor or categorical variable. On the other hand for instance, If your age is continuous (rather than age brackets) then it would be a covariate. If your age is given as age-brackets, then it wont be covariate.