ผลต่างระหว่างรุ่นของ "Probstat/week5 practice 1"

จาก Theory Wiki
ไปยังการนำทาง ไปยังการค้นหา
แถว 1: แถว 1:
 
== Practice exercises ==
 
== 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)''.
 
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)''.
 +
 +
2. Let random variable ''X'' be the outcome after tossing a fair die (with 6 faces of values 1,2,3,...,6).  Find E[''X''] and ''Var(X)''.
 +
 +
3. You have observed the distribution of the score for a probability class.  You notice that, from an exercise, students get 5 points with probability 0.1, 4 points with probability 0.2, 3 points with probability 0.3, 2 points with probability 0.1, 1 point with probability 0.2, and 0 points with probability 0.1.  Let random variable ''X'' be the points a student will get.  Find E[''X''] and ''Var(X)''.
  
 
== Theoretical exercises ==
 
== Theoretical exercises ==

รุ่นแก้ไขเมื่อ 02:37, 16 กันยายน 2557

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).

2. Let random variable X be the outcome after tossing a fair die (with 6 faces of values 1,2,3,...,6). Find E[X] and Var(X).

3. You have observed the distribution of the score for a probability class. You notice that, from an exercise, students get 5 points with probability 0.1, 4 points with probability 0.2, 3 points with probability 0.3, 2 points with probability 0.1, 1 point with probability 0.2, and 0 points with probability 0.1. Let random variable X be the points a student will get. Find E[X] and Var(X).

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