ผลต่างระหว่างรุ่นของ "Probstat/week5 practice 1"
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| + | == Practice exercises == | ||
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== Theoretical exercises == | == Theoretical exercises == | ||
1. For a random variable ''X'' with variance ''Var(X)''. For a constant ''a'', prove that <math>Var(aX) = a^2 Var(X)</math>. | 1. For a random variable ''X'' with variance ''Var(X)''. For a constant ''a'', prove that <math>Var(aX) = a^2 Var(X)</math>. | ||
2. For a non-negative discrete random variable <math>X</math> that takes on values 0,1,2,..., show that <math>\mathrm{E}[X] = \sum_{i=0}^{\infty} P\{ X\geq i \}</math>. | 2. For a non-negative discrete random variable <math>X</math> that takes on values 0,1,2,..., show that <math>\mathrm{E}[X] = \sum_{i=0}^{\infty} P\{ X\geq i \}</math>. | ||
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Practice exercises
Theoretical exercises
1. For a random variable X with variance Var(X). For a constant a, prove that .
2. For a non-negative discrete random variable that takes on values 0,1,2,..., show that .
![{\displaystyle \mathrm {E} [X]=\sum _{i=0}^{\infty }P\{X\geq i\}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/33b72e076a079c5d16d403a9b6801a319a2a01f8)
