Project ForgeEngineering Mathematics
Probability & Statistics
GATE 2011
Hard
Fuel cell stacks are made of NINE membrane electrode assemblies (MEAs) interleaved between TEN bipolar plates (BPs). The widths of MEA and BP are normally distributed with μMEA=0.15, σMEA=0.01 and μBP=5, σBP=0.1 respectively, and are independent of each other. Which ONE of the following represents the CORRECT values of (μstack, σstack) for the overall fuel cell stack width?
- (51.35, 0.32)
- B(51.35, 1.09)
- C(5.15, 0.10)
- D(5.15, 0.11)
Explanation
μstack=9×μMEA+10×μBP=9×0.15+10×5=1.35+50=51.35. For independent sums, variances add: σstack²=9×σMEA²+10×σBP²=9×0.0001+10×0.01=0.1009, so σstack≈0.318≈0.32.
Source: GATE CH 2011 (2011)
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