This exercise demonstrates that, in general, the results provided by Tchebysheff's theorem cannot be improved upon. Let Ybe a random variable such that p(-1) = . p(1) = . p (0) = %3D a Show that E(Y) = 0 and V(Y) = 1/9. b Use the probability distribution of Yto calculate P (|Y – µ| 30). Compare this exact probability with the upper bound provided by Tchebysheff's theorem to see that the bound provided by Tchebysheff's theorem is actually attained when k= 3. *c In part (b) we guaranteed E(Y) = 0 by placing all probability mass on the values -1, 0, and 1, with p(-1)% 3 p(1). The variance was controlled by the probabilities assigned to p(-1) and p(1). Using this same basic idea, construct a probability distribution for a random variable X that will yield P (X- ux|2 2ox) = 1/4. f any k>1 is specified, how can a random variable Wbe constructed so that P (W-HwlZ kow) = 1/k2?

This exercise demonstrates that, in general, the results provided by Tchebysheff's theorem cannot be improved upon. Let Ybe a random variable such that p(-1) = . p(1) = . p (0) = %3D a Show that E(Y) = 0 and V(Y) = 1/9. b Use the probability distribution of Yto calculate P (|Y – µ| 30). Compare this exact probability with the upper bound provided by Tchebysheff's theorem to see that the bound provided by Tchebysheff's theorem is actually attained when k= 3. *c In part (b) we guaranteed E(Y) = 0 by placing all probability mass on the values -1, 0, and 1, with p(-1)% 3 p(1). The variance was controlled by the probabilities assigned to p(-1) and p(1). Using this same basic idea, construct a probability distribution for a random variable X that will yield P (X- ux|2 2ox) = 1/4. f any k>1 is specified, how can a random variable Wbe constructed so that P (W-HwlZ kow) = 1/k2?

Name: c and d please! This exercise demonstrates that, in general, the resul
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Description: c and d please! This exercise demonstrates that, in general, the results providedby Tchebysheff's theorem cannot be improved upon. Let Ybe arandom variable such thatp(-1) = –, p (0) = º, p(1) ==18 P(1) =18a Show that E(Y) = 0 and V(Y) = 1/9.b Use the

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter14: Counting And Probability

Section14.2: Probability

Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...

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