GATE 2022 ST – Question 26

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

X has PMF P(X=x)=(3/4)^(x−1)/4,x=1,2,… . Evaluate Σ from n=0 to ∞ of P(n<X≤n+3),to two decimals.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 2.30 to 2.32

Explanation

The geometric tail is P(X>n)=(3/4)^n. Each summand is (3/4)^n[1−(3/4)³]. Summing the geometric series gives [1−27/64]/(1−3/4)=37/16=2.3125,rounded **2.31**.

More Discrete Distributions questions

GATE 2021 ST Q41 – X is Poisson with E X²=110. Which claim is NOT true?
GATE 2026 ST Q27 – For n≥7, X has probabilities P(X=i)=2P(X=i−1),i=2,…,n, summing to 1 over i=1,…,n. Find…
GATE 2026 ST Q42 – X has support 0,1,2,… and P(X≥k+1 X≥k)=p for every k≥0,0<p<1. Which holds?
GATE 2025 ST Q14 – For X~Poisson(ln2), find E[e((ln3)X)].
GATE 2025 ST Q29 – For X~Binomial(2,1/3), find 18E(X²) (integer).
GATE 2024 ST Q31 – X~Poisson(λ),λ>0, satisfies P(X=4)=2P(X=5). If P(X=α) is its maximum mass, find α…

All Discrete Distributions questions →