Unformatted text preview: You are told to assume that the quality of each bulb is independent, and identically distributed. (a) Supposing you test n randomly picked bulbs, what is a good estimate for p , Z n , such that Z n converges to p in probability? (b) The management asks that the estimate is located in the range p ± . 1 with probability 0.95. Are 27 randomly picked bulbs enough for this speciFcation? Give the reason. 3. p X (x) n p Y n 1 1 1 1 n n 1 n1 n (y) 1 x n y Let X n and Y n have the distributions shown above. (a) Evaluate the expectation and variance for X n and Y n . (b) What does the Chebyshev inequality tell us about the convergence of X n ? (c) What does the Chebyshev inequality tell us about the convergence of Y n ? (d) Is X n convergent in probability? If so, to what value? Explain. (e) Is Y n convergent in probability? If so, to what value? Explain....
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This note was uploaded on 12/08/2010 for the course MATH 6.041 / 6. taught by Professor Muntherdahleh during the Spring '10 term at MIT.
 Spring '10
 MuntherDahleh
 Systems Analysis, Probability

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