Answer: Distribution of their sum.
- A Product of their PDFs
- B Distribution of their sum
- C Distribution of their difference only
- D Their joint distribution
Correct answer: B. Distribution of their sum
Explanation: Convolution: if X, Y independent with PDFs f and g, the PDF of Z=X+Y is h(z) = ∫f(x)g(z−x)dx = (f*g)(z). Example: sum of two independent normals is normal. MGF approach: M<sub>X+Y</sub>(t) = M<sub>X</sub>(t)·M<sub>Y</sub>(t). Answer: distribution of their sum.
Venn diagram of the universal set U with events A and B, showing the intersection (A and B), the parts unique to each event, and the complement region outside both.
Concept context
Chance, events, conditional probability, and Bayes theorem