Use P(A UBU)PCA) +P(B) + P(AnB)-This gives (-1)k+1 ㄧㄨㄧㄧ-)+ k=1 1--~ 0.632121 k! Homework Your assignment is to show how we get these last two equalities.
V n balls are numbered one through n; draw them (without replacement); what is the probability that at least one ball will be drawn with its number equal to the number of balls drawn? As n -oo what is the probability? Use P(A U BU...)P(A) +P(B) +-P(AnB)- This gives -1)1 n n-1 = 1 ~-~ 0.632121 kl Your assignment is to show how we get these last two equalities
5. Stirling's approximation gives an approximate value for the factorial n! n! xVannne-n n! V2πηη"e-n which means that lim Moreover. V2rnnne--+ 1/(12叶1) < n! < V2mn"e-n+1/12n for all n>1 . a- Show that lim b- We toss a fair coin 100 times. Find an approximate value for the following probability P(we get exactly 50 heads ).
\ Can anyone explain a and b how they got this answer. what formula they use P-8.2 For each ofthe following 10-point DF「s, determine a formula the l0-point IDFT Use MATLAB to check your work numerically. 1に0 (a) Xa[k] = 0 k = 1, 2, . . . ,9 (b) Xolk-1 for k = 0, 1,2, ,9 (c)Xc[k] =10 k = 0,1,2, 4, 5, 6, 8, 9 (d) Xalk]cos(2mk/5) for k 0,1,2,...,9 k=3, 7 I (a) Substituting into the inverse...
please answer #6 a and b, my 6d from previous assignment is shown in 2nd picture 6. a. Show that if N E C(H) is nilpotent then ơr(N) 0, (use 6d fron last assignment). b. List the similarity classes of the (nonzero) nipotent linear maps of a 5- dimensional vector space overE i.e., give a representative matrix in each class) d) N is nilpotent z-3n such that Nn , D T-Nisinvertible wit'h inverse ANAN . 6. a. Show that if...
Problem 3. Show the formula P((An B)U(A n B))- P(A) +P(B)-2P(AnB), which givgs the probability that exactly one of the events A and B will occur. [Compare with the formula P(AU B) P(A) P(B) - P(AnB), which gives the probability that at least one of the events A and B will occur.]
1. (a) What is the normalızation condition for the probability P(u) (b) Iffu) and g(u) are any two functions of u then, show that f(u)+ g(u)f(u)+g(u) (3) (c) Calculate the mean values for the random walk problem (t) Mean number for (a) nght and (b) left steps (u) Mean displacement (10) (3) (7) (1) Dispersion of the net Hint: displacement to the right N! w(n)n (N-n)p"qN where N is the total number of steps, n the number of steps to...
Do A and used C as question say A. (This problem gives an explanation for the isomorphism R 1m(A) R"/1m(A'), where A, Q-IAP, with Q and P invertible.) Let R be a ring and let M, N, U, V be R-modules such that there existR module homomorphisms α : M N, β : u--w, γ: M-+ U and δ: N V such that the following diagram is commutative: (recall that commutativity of the diagram means that δ ο α γ)...
Q3 (Prove that P∞ k=1 1/kr < ∞ if r > 1) . Let f : (0,∞) → R be a twice differentiable function with f ''(x) ≥ 0 for all x ∈ (0,∞). (a) Show that f '(k) ≤ f(k + 1) − f(k) ≤ f '(k + 1) for all k ∈ N. (b) Use (a), show that Xn−1 k=1 f '(k) ≤ f(n) − f(1) ≤ Xn k=2 f '(k). (c) Let r > 1. By finding...
6. We want to use the Integral Test to show that the positive series a converges. All of the following need to be done except one. Which is the one we don't need to do? (a) Find a function f(x) defined on [1,00) such that f(x) > 0, f(x) is decreasing, and f(n) = a, for all n. (b) Show that ſ f(z) dr converges. (e) Show that lim Ss6 f(x) dx exists. (d) Show that lim sexists. 7. Suppose...