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proving that $\sum_{k=1}^{n}\frac{k}{2^{n + 1 - k}} = n + \frac{1}{2^n} - 1$. (full problem in the post)

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#combinatorics #induction #expected-value
103
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A question about conditional expectation $E[X_1 | X_1 + X_2]$

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#probability #probability-theory #expected-value #conditional-expectation
29
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Which method should I use to solve the statistic optimization problem?

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#statistics #optimization #numerical-methods #algorithms #expected-value
41
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Show that $plim A_n = plim B_n$ implies $plim V(A_n) = plim V(B_n)$

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#measure-theory #asymptotics #expected-value #variance
28
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Calculate the correlation coefficient

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#probability #random-variables #expected-value #covariance #correlation
42
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Could someone explain the concept behind the expected length of a second run in a sequence of bernoulli trials?

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#probability-theory #expected-value #conditional-expectation #geometric-distribution
60
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Expected value of maximum of n independent dice rolls

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#expected-value
78
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Two different approaches to find expectation yield different results

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#probability #expected-value #conditional-expectation #variance
30
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Calculate the mean number of survivors of a randomly selected insect

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#probability-theory #solution-verification #expected-value #poisson-distribution #exponential-distribution
46
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When is E[X | X > Y] defined?

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#random-variables #expected-value #conditional-expectation
53
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Dealing with indefinite integrals when using Least Squares Estimation

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#probability #statistics #improper-integrals #expected-value #least-squares
87
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Why is this conditional expectation equal to this probability?

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#probability #stochastic-processes #expected-value #conditional-probability
62
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Is Carleman's condition a sufficient condition for Hausdorff moment problem

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#probability-theory #expected-value #moment-problem
240
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Expected number of non-uniform draws until collision?

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#probability #expected-value #multinomial-distribution
54
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Existence of an integral that looks like the rth order moment

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#probability-theory #probability-distributions #definite-integrals #expected-value #moment-generating-functions

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