GATE 2025 ST – Question 59
Service densities at pumps P₁,P₂ are λe^(−λx) and λ²xe^(−λx),x>0. Each pump is selected with probability 1/2. If the chance of service exceeding one minute is 2e⁻², find λ>0 (integer).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 2 to 2
Explanation
The two survival probabilities at 1 are e⁻λ and (1+λ)e⁻λ. Their mixture is [(2+λ)/2]e⁻λ. Equating to 2e⁻² gives λ=2. This is unique because the mixture derivative is −(1+λ)e⁻λ/2<0 for λ>0. **2**.