IAI Actuarial Core Principles · Actuarial Statistics · Jointly distributed random variables
X has a Poisson distribution with mean 3. Given X=x, Y is binomial with x trials and success probability 0.4. What is E[Y]?
E[Y] is 1.2. By the tower property, E[Y] equals E[0.4X], which is 0.4 times the Poisson mean of 3. Thinning a Poisson count by 0.4 scales the mean accordingly.
- A0.4
- B1.2Correct
- C1.8
- D2.4
- 3.0
Explanation
E[Y|X]=0.4X, so E[Y]=0.4*E[X]=0.4*3=1.2 by the tower property. Option 2.4 wrongly uses 0.8 and 3.0 ignores the thinning.
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