Let α,β,γ denote words of length n; d(α,β) denotes the distance between the words α and β. Prove the following triangle inequality:
d(α, γ) ≤ d(α, β) + d(β, γ)
Let α,β,γ denote words of length n; d(α,β) denotes the distance between the words α and...
1. Let the angles of a triangle be α, β, and γ, with opposite sides of length a, b, and c, respectively. Use the Law of Sines to find the remaining sides. (Round your answers to one decimal place.) α = 48°; β = 83°; c = 112 a= b= 2. Let the angles of a triangle be α, β, and γ, with opposite sides of length a, b, and c, respectively. Use the Law of Sines to find the remaining sides....
b. Suppose ~ Γ(α, β), with α > 0, β > 0 and let Y-eu. Find the probability density function of Y Find EY and var(Y)
Suppose X and Y are independent and Prove the following a) U=X+Y~gamma(α + β,γ) b) V=X/(X + Y ) ∼ beta(α,β) c) U, V independent d) ~gamma(1/2, 1/2) when W~N(0,1) X ~ gammala, y) and Y ~ gamma(6, 7) We were unable to transcribe this image
Let α, β, γ ∈ ℝ designate pairwise different real numbers and understand the ℝ-vectorspace P3(ℝ) of real polynomials of degree 2 or less as an inner product space via. = p(α)q(α) + p(β)q(β) + p(γ)q(γ). Now let λ ∈ C / ℝ designate a complex number which is NOT a real number. Question: Show that for every p, q ∈ P3(ℝ) it holds that is a real number. (Hint: show that the number doesn't change through complex conjugation. (NOTE:...
Exercise 2. Let (an) be a sequence, and α, β ε R such that α β. Suppose there exists N N such that for all n2 N Then for allm2 N, Give an example demonstrating that it is not necessarily true that for all m2 N sup{an : n > m} < β Exercise 2. Let (an) be a sequence, and α, β ε R such that α β. Suppose there exists N N such that for all n2 N...
Let 0 < γ < α . Then a 100(1 − α )% CI for μ when n is large is Xbar+/-zγ*(s/sqrt(n))The choice γ = α /2 yields the usual interval derived in Section 8.2; if γ ≠ α /2, this confidence interval is not symmetric about . The width of the interval is W=s(zγ+ zα-γ)/sqrt(n). Show that w is minimized for the choice γ = α /2, so that the symmetric interval is the shortest. [ Hints : (a)...
If three sentences of TFL, α, β and γ, are jointly inconsistent, what is (a Λ β) ^ (3) a. A tautology. b. A contradiction. c. A contingent sentence. d. Not enough information to decide. If three sentences of TFL, α, β and γ, are jointly inconsistent, what is (a Λ β) ^ (3) a. A tautology. b. A contradiction. c. A contingent sentence. d. Not enough information to decide. If three sentences of TFL, α, β and γ, are...
Let C' be a binary code of length n and distance d 2t +1. Prove that 2" Let C' be a binary code of length n and distance d 2t +1. Prove that 2"
Let α and β be real numbers with 0 < α < βく2m and let h : [α, β] → R>o be a continuous function that is always positive. Define Rh,a to be the region of the (x,y)-plane bounded by the following curves specified in polar coordinates: r-h(0), r-2h(0), θ α, and θ:# β. 3. (a) Show that (b) (c) depends only on β-α, not on the function h. Evaluate the above integral in the case where α = π/4...
inal point β. Show plex constan I. Let γ be a directed smooth curve with initial point α and term directly from Definition 3 that f c dz-c(β-α), where c is any contioninge® Does the same formula hold for integration along an arbitrary con β? Definition 3. Let f be a complex-valued function defined on the ined on the directed smooth curve y. We say that f is integrable along y if there complex number L that is the limit...