statistical inference

Problem 1 Part (a) Part (b) Part (c) Interpretation Part (d) Part (e) Part (f) Part (g) Part (h) Problem 2 Part (a) Part (b) Part (c) Part (d) Interpretation Part (e) Appendix: code mixed.

Problem 1 Solution: Newton’s method Solution: Secant method Comparison of Newton’s method versus secant method Problem 2 Solution Problem 3 Solution: part (a) Solution: part (b) Problem 4 Solution Problem 5 Solution Problem 6 Solution Problem 1 Write your own code and find solution to the equation $x^3+x-4=0$ using Newton’s method and the secant method.

Problem 1 Part (a) Part (b) Part (c) E-step M-step Part (d) Problem 2 Part (a) E-step M-step Part (b) Part (c) Problem 1 Derive the E-M algorithm for right-censored normal data with known variance, say $2=1$.

Problem 1 Part (a) Acceptance-rejection sampler Metropolis-Hastings algorithm Part (b) Part (c) Problem 2 (Problem 7.1) Part (a) Part (b) Numerical imprecision Part (c) Part (d) Part (e) Problem 3 Part (a) Part (b) Distribution of $\mu |(\tau ,\overrightarrow{x})$ Distribution of $\tau |(\mu ,\overrightarrow{x})$ Part (c) Additional analysis Problem 1 Use Metropolis Hasting algorithm to generate $Y\sim \mathrm{GAM}(\alpha ,1)$, where $\alpha >1$.

Problem 1 Part (a) Part (b) Part (c) Interpretation Part (d) Comparing machines Comparing machine $\times$ operator Part (e) Problem 2 Part (a) Part (b) Part (c) Interpretation Part (d) Part (e) Part (f) Appendix: Code Problem 1 The surface finish of metal parts made on $a=4$ machines is under investigation.