Skip to content

IAI Actuarial Core Principles · Actuarial Statistics · Jointly distributed random variables

The joint probability function of X and Y is P(X=0,Y=0)=0.1, P(X=0,Y=1)=0.3, P(X=1,Y=0)=0.2 and P(X=1,Y=1)=0.4. What is E[Y | X=1]?

E[Y | X=1] is 0.667. Given X=1, the marginal probability is 0.6, and the probability that Y=1 is 0.4 divided by 0.6, which is two thirds. Because Y is an indicator, its conditional mean equals that conditional probability.

  1. A0.4
  2. B0.5
  3. C0.6
  4. D0.667Correct
  5. 0.7

Explanation

P(X=1)=0.2+0.4=0.6. P(Y=1|X=1)=0.4/0.6=2/3. Since Y is 0 or 1, E[Y|X=1]=0.667. The value 0.4 is the joint probability, which forgets to divide by P(X=1).

Did you get it right without looking?

One question tells you little. A timed set on Jointly distributed random variables shows your real accuracy, how long you take and where you lose marks.

Practise Jointly distributed random variablesFree diagnostic mock

More Jointly distributed random variables questions