ผลต่างระหว่างรุ่นของ "Probstat/week5 practice 1"

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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>.
  
== Programming exercise: the fullest bins ==
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== Programming exercises ==
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=== The fullest bins ===
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=== Distribution of th binomial random variables ===

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Practice exercises

1. Consider a random variable Z that becomes 1 with probability 1/3, 0 with probability 1/3, and 1 with probability 1/3. Find E[Z], and Var(Z).

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 .

Programming exercises

The fullest bins

Distribution of th binomial random variables