ผลต่างระหว่างรุ่นของ "Probstat/week5 practice 2"

รุ่นแก้ไขเมื่อ 17:21, 17 กันยายน 2557

This is part of probstat.

1. Consider a simple experiment of choosing, uniformly at random, an integer from the set {0,1}.

1.1 Let X be a random variable that denotes the chosen integer from the experiment. Find E[X] and Var(X).
1.2 Let's perform the experiment 2 times. Let X₁ and X₂ be random variables that denote the chosen integers from the first and the second experiments. Let Y = (X₁ + X₂)/2. Find E[Y] and Var(Y).
1.3 Let's perform the experiment K times. Let X₁, X₂,... X_K be random variables that denote the chosen integers from each experiments. Let Z = (X₁ + ... + X_K)/K. Find E[Z] and Var(Z).
1.4 Compare these 3 random variables. I.e., compare E[X], E[Y], and E[Z], and also Var(X), Var(Y), and Var(Z). What is the effect of the number independent trials to the variance. What does it actually mean?

@@ แถว 7: / แถว 7: @@
 * 1.1 Let ''X'' be a random variable that denotes the chosen integer from the experiment.  Find E[''X''] and ''Var(X)''.
 * 1.2 Let's perform the experiment 2 times.  Let ''X''<sub>1</sub> and ''X''<sub>2</sub> be random variables that denote the chosen integers from the first and the second experiments.  Let ''Y'' = (''X''<sub>1</sub> + ''X''<sub>2</sub>)/2.  Find E[''Y''] and ''Var(Y)''.
-* 1.2 Let's perform the experiment ''K'' times.  Let ''X''<sub>1</sub>, ''X''<sub>2</sub>,... ''X''<sub>K</sub>  be random variables that denote the chosen integers from each experiments.  Let ''Z'' = (''X''<sub>1</sub> + ... + ''X''<sub>K</sub>)/K.  Find E[''Z''] and ''Var(Z)''.
+* 1.3 Let's perform the experiment ''K'' times.  Let ''X''<sub>1</sub>, ''X''<sub>2</sub>,... ''X''<sub>K</sub>  be random variables that denote the chosen integers from each experiments.  Let ''Z'' = (''X''<sub>1</sub> + ... + ''X''<sub>K</sub>)/K.  Find E[''Z''] and ''Var(Z)''.
+* 1.4 Compare these 3 random variables. I.e., compare E[''X''], E[''Y''], and E[''Z''], and also ''Var(X)'', ''Var(Y)'', and ''Var(Z)''.  What is the effect of the number independent trials to the variance.  What does it actually mean?