Respuesta :
Answer:
[tex] E(X) = 7*0.18 +9*0.08 +11*0.09 +15*0.08 +17*0.41 =13.22[/tex]
And we can find the second moment with this formula:
[tex] E(X^2) = \sum_{i=1}^n X^2_i P(X_i)[/tex]
And replacing we got:
[tex] E(X^2) = 7^2*0.18 +9^2*0.08 +11^2*0.09 +15^2*0.08 +17^2*0.41 =189.72[/tex]
And we can find the variance like this:
[tex] Var(X) = E(X^2) -[E(X)]^2= 189.72- (13.22)^2 =14.9516[/tex]
And the deviation would be:
[tex] Sd(X)= \sqrt{14.9516}= 3.867[/tex]
Step-by-step explanation:
For this case we have the following dataset given:
Payment $7 $9 $11 $13 $15 $17
Probability 0.18 0.08 0.09 0.16 0.08 0.41
For this case we can calculate the mean with this formula:
[tex] E(X) = \sum_{i=1}^n X_i P(X_i)[/tex]
And replacing we got:
[tex] E(X) = 7*0.18 +9*0.08 +11*0.09 +15*0.08 +17*0.41 =13.22[/tex]
And we can find the second moment with this formula:
[tex] E(X^2) = \sum_{i=1}^n X^2_i P(X_i)[/tex]
And replacing we got:
[tex] E(X^2) = 7^2*0.18 +9^2*0.08 +11^2*0.09 +15^2*0.08 +17^2*0.41 =189.72[/tex]
And we can find the variance like this:
[tex] Var(X) = E(X^2) -[E(X)]^2= 189.72- (13.22)^2 =14.9516[/tex]
And the deviation would be:
[tex] Sd(X)= \sqrt{14.9516}= 3.867[/tex]
