EXERCISE 6.1.1 3 Let p, q E X and γ : [0, 1]- X a path from p to q. a. For a loop α in X based at p, show that γ-1αγ s a loop based at q b. Show that the map [a] -+ [γ_ιαγ] is a group isomorphism from π1(X, p) to π1(X, q). EXERCISE 6.1.1 3 Let p, q E X and γ : [0, 1]- X a path from p to q. a. For a...
let X=pareto(α,γ) find the distribution and density function of Y=logX
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)
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....
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)
Find irr(α, Q) and deg(α, Q), where α = √ 2 + i.
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:...
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)...
Verify that the probability density function of Γ(α,λ) inte- grates to 1.
.Suppose X~Gamma(α,γ). What are the first and second population moments of X?