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Part BCSIR NET December 2023mgf-factorisation

Mgf factorisation

Let (X, Y) have joint moment generating function M(t1,t2)=(3/4+M(t_{1}, t_{2}) = (3/4 + et1/4)2e^{t_{1}}/4)^{2} (5/6 + et2/6)3e^{t_{2}}/6)^{3}. Then P(X + 2Y > 1) equals

  1. A.1581/3456✓ Correct
  2. B.1875/3456
  3. C.125/3456
  4. D.3331/3456

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests moments and tails.

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50 are analysed free — try those first.

The trap it tests

Moments and tails

A moment assumed to exist, or tail behaviour assumed to be tame.

Drill statements like this

Related counterexample: Uncorrelated ⇒ independent

More on this topic

The chapter behind this: Random variables, moments and generating functions — free to read

From Probability › Random variables, distributions, moments, MGF

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