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Expectation of the norm of a Gaussian vector raised to a power

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#probability #statistics #multinomial-coefficients #expected-value #multinomial-theorem
202
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A proof on multinomial roots

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#polynomials #summation #roots #geometric-progressions #multinomial-theorem
124
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Using Bayes' with a Multinomial Distribution

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#probability #probability-distributions #bayesian #multinomial-theorem
2.8k
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Expansion of the cube of the sum of N numbers

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#polynomials #summation #cubics #multinomial-coefficients #multinomial-theorem
203
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Sum of coefficients in multinomial expansion

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#multinomial-theorem
309
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Weighted sum of product of binomial coefficients

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#summation #binomial-coefficients #binomial-theorem #multinomial-theorem
91
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Why can’t we use multinomial theorem here?

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#combinatorics #combinations #multinomial-theorem
66
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Finding sum multinomial

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#sequences-and-series #binomial-coefficients #multinomial-theorem
91
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Trinomial expansion with power constraints

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#combinatorics #multinomial-theorem
82
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How to prove $\sum_{\alpha_1=0}^k \sum_{|\alpha|=k} \dfrac{k!}{\alpha!} a^\alpha = \sum_{|\alpha|=k} \dfrac{k!}{\alpha!} a^\alpha$

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#summation #multinomial-coefficients #multinomial-theorem
104
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Evaluating a sum involving multinomial coefficient

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#summation #binomial-coefficients #multinomial-coefficients #multinomial-theorem
72
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Simplifying summation of binomials

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#markov-chains #random-walk #binomial-distribution #multinomial-theorem
977
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Sum of dependent Binomial distributions

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#probability #binomial-coefficients #binomial-distribution #multinomial-theorem
111
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Multinational Coefficient Difficulty

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#discrete-mathematics #multinomial-coefficients #multinomial-theorem
3.8k
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if in the expansion of $(1+x)^m (1-x)^n$, the coefficients of $x$ and $x^2$ are $3$ and $-6$. Find value of $m$ and $n$.

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#polynomials #binomial-theorem #multinomial-theorem

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