GATE 2024 ST – Question 31

Standard Univariate Distributions · Discrete Distributions · 1 mark · Numerical answer

X~Poisson(λ),λ>0, satisfies P(X=4)=2P(X=5). If P(X=α) is its maximum mass, find α (integer).

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Correct answer: 2 to 2

Explanation

The ratio P(X=5)/P(X=4)=λ/5 equals 1/2, so λ=2.5. For a noninteger Poisson mean the unique mode is floor λ=**2**, as consecutive mass ratios cross 1 after this index.

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