Question

Prob (X = 1) = ¼, Prob (X = 2) = ½, Prob (X = 3) = ¼, where Prob (X = k) is the probability that X = k, for k = 1, 2, and 3. What is the variance of X?

Answer 1

Answer:

$E(X)=\sum_{i=1}^n X_i P(X_i) = 1*0.25 +2 *0.5 +3*0.25= 2$

We can calculate the moment of second order and we got:

$E(X^2)=\sum_{i=1}^n X^2_i P(X_i) = 1^2*0.25 +2^2 *0.5 +3^2*0.25= 4.5$

And we can calculate the variance like this:

$Var(X) = E(X^2) -[E(X)]^2 = 4.5 -(2)^2 =0.5$

And the deviation would be:

$Sd(X) = \sqrt{0.5}=0.707$

Step-by-step explanation:

For this case we have the following distribution:

X       1,       ,2,     3

P(X) 0.25,  0.5, 0.25,

We can calculate the expected value with this formula:

$E(X)=\sum_{i=1}^n X_i P(X_i) = 1*0.25 +2 *0.5 +3*0.25= 2$

We can calculate the moment of second order and we got:

$E(X^2)=\sum_{i=1}^n X^2_i P(X_i) = 1^2*0.25 +2^2 *0.5 +3^2*0.25= 4.5$

And we can calculate the variance like this:

$Var(X) = E(X^2) -[E(X)]^2 = 4.5 -(2)^2 =0.5$

And the deviation would be:

$Sd(X) = \sqrt{0.5}=0.707$