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📐 Mathematics  ·  Probability  ·  JEE

The convolution of two independent distributions gives:

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.

UABA and BA onlyB onlyOutside both circles: complement of (A union B)

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

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