Part CCSIR NET December 2024read-the-distribution-off-the-generating-function

Read the distribution off the generating function

Let X and Y be independent random variables with the moment generating functions M_X(t) = (1/9)(2 + eᵗ $)^{2}, t \in R$ and M_Y(t) = exp[eᵗ $- 1], t \in R$ , respectively. Then, which of the following statements are true?

A.P(XY = 0) = (4 + 5e⁻ $^{1}) /9$ ✓
B. $E [(3 X - Y)^{2}] = 6$ ✓
C.Var(X + Y) = 2
D.Cov(2X + Y, X − 2Y) = −10/9✓

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.

See pricing

50 are analysed free — try those first.

Related counterexample: Uncorrelated ⇒ independent

Read the distribution off the generating function

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