GATE DA 2026 Set 1 — Question 45
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Calculus & Optimization → Discrete Random Variables → Central Limit Theorem
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Question
LetWhich of the following is the value of ?
Correct answer
(A) 0.5
Solution
The expression represents the probability where is a Poisson random variable with mean .
According to the Central Limit Theorem, as , the Poisson distribution can be approximated by a Normal distribution .
Let . Then converges in distribution to a standard normal variable .
.
As , .
Thus, .
According to the Central Limit Theorem, as , the Poisson distribution can be approximated by a Normal distribution .
Let . Then converges in distribution to a standard normal variable .
.
As , .
Thus, .
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