In Exercises 5–8, use the relatively small number of given bootstrap samples to construct the confidence interval.
7. Freshman 15 Here is a sample of amounts of weight change (kg) of college students in their freshman year (from Data Set 6 “Freshman 15” in Appendix B): 11, 3, 0, −2, where −2 represents a loss of 2 kg and positive values represent weight gained. Here are ten bootstrap samples: {11, 11, 11, 0}, {11, −2, 0, 11}, {11, −2, 3, 0}, {3, −2, 0, 11}, {0, 0, 0, 3}, {3, −2, 3, −2}, {11, 3, −2, 0}, {−2, 3, −2, 3}, {−2, 0, −2, 3}, {3, 11, 11, 11}.
a. Using only the ten given bootstrap samples, construct an 80% confidence
b. Using only the ten given bootstrap samples, construct an 80% confidence interval estimate of the standard deviation of the weight changes for the population.
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- 5. Suppose that X is an integer valued random variable, and let mЄ N. Show that 8 11118 P(narrow_forward食食假 6. Show that I(AUB) = max{1{A}, I{B}} = I{A} + I{B} - I{A} I{B}; I(AB)= min{I{A}, I{B}} = I{A} I{B}; I{A A B} = I{A} + I{B}-21{A} I{B} = (I{A} - I{B})². -arrow_forward11. Suppose that the events (An, n ≥ 1) are independent. Show that the inclusion- exclusion formula reduces to P(UAL)-1-(1-P(Ak)). k=1 k=1arrow_forward12. (a) Explain tail events and the tail o-field. Give an example.arrow_forwardLet A, A1, A2,... be measurable sets. Then P(A)=1- P(A); • P(Ø) = 0; P(A1 UA2) ≤ P(A1) + P(A2); A1 C A2 P(A1) P(A2); P(UA) + P(n=14) = 1. Exercise 3.1 Prove these relations. ☐arrow_forward17. Suppose that X1, X2,..., Xn are random variables, such that E|xk| < ∞ for all k, and set Yn = max1arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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