GATE 2024 ST – Question 17

Probability · Random Variables and Transforms · 1 mark · Multiple choice

X takes only values 1,2 and E X=10/7. Find the fourth derivative of its MGF at zero.

Show answer and explanation

Correct answer: (A) 52/7

Explanation

Let p=P(X=2). Then E X=1+p=10/7, so p=3/7 and P(X=1)=4/7. The fourth MGF derivative is E X⁴=(4/7)·1+(3/7)·16=**52/7, A**.

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