ผลต่างระหว่างรุ่นของ "Probstat/week5 practice 1"
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Jittat (คุย | มีส่วนร่วม) |
Jittat (คุย | มีส่วนร่วม) |
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| แถว 7: | แถว 7: | ||
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 | + | == Programming exercises == |
| + | === The fullest bins === | ||
| + | |||
| + | === Distribution of th binomial random variables === | ||
รุ่นแก้ไขเมื่อ 02:02, 16 กันยายน 2557
เนื้อหา
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 .
![{\displaystyle \mathrm {E} [X]=\sum _{i=0}^{\infty }P\{X\geq i\}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/33b72e076a079c5d16d403a9b6801a319a2a01f8)
