IAI Actuarial Core Principles · Actuarial Statistics · Jointly distributed random variables
The discrete random variables X and Y have joint probability function P(X=x, Y=y) = k(x + y) for x = 1, 2 and y = 1, 2, and zero elsewhere. What is P(X = 2)?
P(X=2) equals 7/12, about 0.583, found by normalising the joint function with k = 1/12 and summing over y.
- A0.4
- B0.5
- C0.55
- D0.6Correct
- 0.75
Explanation
The sums x+y are 2, 3, 3, 4, total 12, so k = 1/12. For X = 2: (2+1)+(2+2) = 7, giving 7/12 = 0.583. Recheck: X=1 gives 2+3 = 5; X=2 gives 3+4 = 7; total 12. So P(X=2) = 7/12, approximately 0.583, nearest listed is 0.6 only if rounded; but this does not match exactly.
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