Poisson distribution + Linear combination

Question 1

Mean

Answer 1

E(aX+-bY)=aE(x)+-bE(Y)

Question 2

Variance

Answer 2

Var(aX+-bY)=a squared Var(x)+b squaredVar(Y)
X has a variance of 12
Y has a variance of 4
Var(X-Y) = 12+4=16
Var (2X+3Y) = 2squared x12 + 3squared x 4= 84
Variance is always a +, never a -
Always square the standard deviation to get variance

Question 3

Comparing

Answer 3

If there are letters on both sides of the inequality “take” the letters from the right to the left
e.g. P(X>Y) = P(X-Y>0)
P(3X<5Y)= P(3X-5Y<0)
P(X>Y+15)= P(X-Y>15)

Question 4

Scaling vs Combing

Answer 4

X1 + X2 = two separate observations
2X= one observation doubled

Question 5

Shifts and Stretches

Answer 5

Shifts (+ or -)
Stretches ( x or divide)