IAI Actuarial Core Principles · Actuarial Statistics · Jointly distributed random variables
The joint probability function of X and Y is P(x,y) = k(x + y) for x = 0, 1, 2 and y = 1, 2. What is the marginal probability P(X = 1)?
The marginal probability P(X=1) is 1/3, which equals 7/21. The joint weights sum to 15, giving k = 1/15, and the x=1 row contributes 2+3 = 5, so 5/15 = 1/3.
- A5/21
- B7/21Correct
- C8/21
- D3/21
- 9/21
Explanation
Sum of (x+y) over all cells: x=0 gives 1+2=3, x=1 gives 2+3=5, x=2 gives 3+4=7, total 15, so k=1/15. P(X=1)=5/15=1/3=7/21. Option 5/21 is wrong because it uses a total of 21 rather than 15 with the x=1 sum of 5.
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