GATE 2026 ST – Question 27

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

For n≥7, X has probabilities P(X=i)=2P(X=i−1),i=2,…,n, summing to 1 over i=1,…,n. Find (2ⁿ−1)P(X=7) (integer).

Show answer and explanation

Correct answer: 64 to 64

Explanation

Write P(X=1)=c. Then P(X=i)=2^(i−1)c and normalization gives c(2ⁿ−1)=1. The seventh probability is 2⁶/(2ⁿ−1). Multiplication gives **64**.

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