10. Prove that P(E UFUG)P(E) P(F) + 2P(EFG). 11. If P(E)9 and P(F).8, show that P(EF...
If P(E)9 and P(F)-.8, show that P(EnF)2.7. I inequality, namely, n general, prove Bonferroni s Use induction to generalized Bonferroni's inequality to n events and show the result.
1. Consider a statistical experiment E: (, F,P) and an event A . Note: A EF. a. Use the axioms of probability to show that P(A) 1-P(A). b. Repeat (a) using the definition of the σ-field. 2. Consider a statistical experiment E: (, F,P) in which a fair coin is flipped successively until the same face is observed on successive flips. Let A = {x: x = 3, 4, 5, . . .); that is, A is the event that...
Question 9 (ii) and Question 10 9. For F as in 8, define N:F-Q by N(a+bv2)--22 (i) Prove that N(a3)-N(a)N(8), for all α, β E F. (ii) Find an element u E F such that N(u)-1 and such that all of the powers un are distinct. 10. Use 9 above to prove that the equation 2-2U2-1 has infinitely many solutions over Q. What can you conclude about the number of solutions over Z. 9. For F as in 8, define...
The tone row from a certain piece of music is p-(5, 8, 0, 4, 7, 10, 2, 6, 9, 11, 1, 3). Show that p = T4(Cg(R(rp)))). p-(5, 8, 0, 4,7, 10, 2, 6,9, 11, 1, 3) I(p) R(rp),- T4(C3(R(p))- eBook The tone row from a certain piece of music is p-(5, 8, 0, 4, 7, 10, 2, 6, 9, 11, 1, 3). Show that p = T4(Cg(R(rp)))). p-(5, 8, 0, 4,7, 10, 2, 6,9, 11, 1, 3) I(p) R(rp),-...
i need help with #13 show all steps 7, 8, 9, 10, 11, 12, 13 and 14 Find the exact area of the surface obtained by rotating the curve about the z-axis. 7. y = z?, 052<2 Answer 27" (145/145 - 1) 8. y =V5-I, 35165 9. y = x+1, 063<3 Answer 10. y = 11+e05:51 11. y = cos 03 Answer 1 12. y 13.5 - 2 + 2)", 1<x<2 Answer
Real analysis 10 11 12 13 please (r 2 4.1 Limit of Function 129 se f: E → R, p is a limit point of E, and limf(x)-L. Prove that lim)ILI. h If, in addition, )o for all x E E, prove that lim b. Prove that lim (f(x))"-L" for each n E N. ethe limit theorems, examples, and previous exercises to find each of the following limits. State which theo- rems, examples, or exercises are used in each case....
6) If E is any countable subset of real numbers prove that A*(E) = A*(E) = 0. 7) Show that the set of all real numbers IR is measurable with >(IR) = . 8) Prove that If f : [a, b] IR is continuous [a; b]then it is measurable [a, b]. 9) Give an example of a function f : [O, 1] IR which is measurable on [O, 1] but not continuos on [O, 1]. 10) Find the Lebesgue integral...
Suppose that E, F, and G are events with P(E) = 8/25 , P(F) = 11/50 , P(G) = 23/100 , E and F are mutually exclusive, E and G are independent, and P(F | G) = 20/23 . Find P(E ∪ F ∪ G).
Please do 10 & 11 Use Intermediate Value Theorem lial p(x) = x4 +7x = 9 has two real root. 8. df Open with Google Docs Then use your calculator to find the ro 9 Let f(z)2with € [0, 00). Find a positive mumber e and two sequences {xn} and {yn} such that lim-(nn) = 0 but |f(xn)- f(Yn)| 2 e. Then conclude that f(x) = x2 is not uniformly continuous on [0, ao) [0, oo). Show that f is...
please do 9 Find a function f(x) with power series f(x) E-1n3 x" 9. 10. Use a power series to show that 0.999...= 1 n(1+1/n) 11. Determine the convergence/divergence of n-11+1/0 12. Find the length of the curve c(t) (Tt+e,2 cos t,2 sin t) for 0t T (1+3) converge? 13. To what value for the sequence an 14. Does the series ne- converge?V 15. Give an example of u, v E R3 perpendicular and with no zero entries in Find...