GATE EE 2014 Set 3 — Question 37
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Engineering Mathematics → Probability → Expectation & Variance
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Question
The mean thickness and variance of silicon steel laminations are 0.2 mm and 0.02 respectively. The varnish insulation is applied on both the sides of the laminations. The mean thickness of one side insulation and its variance are 0.1 mm and 0.01 respectively. If the transformer core is made using 100 such varnish coated laminations, the mean thickness and variance of the core respectively are
Correct answer
(D) 40 mm and 0.24
Solution
1.Mean Thickness Calculation:
- Mean thickness of one silicon steel lamination = mm.
- Mean thickness of varnish insulation on one side = mm.
- Total mean thickness of one coated lamination (1 steel + 2 insulation layers) = mm.
- For 100 such laminations, total mean thickness of the core = mm.
- Variance of one lamination = .
- Variance of insulation on one side = .
- Variance of one coated lamination = .
- For 100 independent laminations, the variance of the core is .
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