2. Is there an element of order 6 in S4? Explain.
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- . Let Dn be as in Example 10. Find a Hamiltonian circuit inCay({(r, 0), (f, 0), (e, 1)}:D4 ⨁ Z5).Does your circuit generalize to the case Dn ⨁ Zn+1 for all n ≥ 4?Let Xi be IID random variables which have the same law as X. Let L(t) = E(e^tX.) Suppose that this is well defined for t ∈ [−1, 1]. Express the moment generating function of the Sum from i=1 to k Xi in terms of k and LSketch the ensemble, that is, realizations of the random process X(t) = A cos(2πft), where f is a uniform random variable U(200, 300). That is, f is uniformly distributed in the range [200, 300] Hz and A = 7 is a constant.
- How to solve this with cohens d using Microsoft Excel Use alpha of 0.05 2 tail. Free Association (in seconds) Partially Controlled (in seconds)5.84 4.844.64 5.643.56 8.565.00 7.002.35 4.353.67 4.677.87 6.677.74 5.444.48 5.586.56 6.26Using the given data. Compute f"(1.8) at O(h²) using Richardson Extrapolation.Let X1,X2,... be a sequence of identically distributed random variables with E|X1|<∞ and let Yn = n−1max1≤i≤n|Xi|. Show that limnE(Yn) = 0
- considering the nonhomogenous 2ndorder ode y'' + 4y = 10sin(9pi x t)Given a random variable X with Moment Generating function M(t), compute the Moment generating functions for the following random variables (in terms of M).In each subpart, k is a scalar.a. k Xb. X + kc. ∑Ni=0 Xi where all Xi are sampled independently from X.d. A random variable Y with PDF(y) = PDF (x + k), both PDF defined over R.e. A random variable Y with PDF(y)=PDF (2x). A research center claims that at least 23% of adults in a certain country think that their taxes will be audited. In a random sample of 900 adults in that country in a recent year, 19% say they are concerned that their taxes will be audited. At α=0.01, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below. (a) Identify the claim and state H0 and Ha.
- Let U₁,..., Un be i.i.d. random variables uniformly distributed in [0, 1] and let Mn = max Ui . 1<i<n Find the cdf of Mn, which we denote by G (t), for t = [0, 1]. For t = [0, 1], G (t) = Now, let Fn (t) denote the cdf of n (1 - Mn); for t > 0, compute lim F₁ (t) =Let X1, X2, ... , Xn be a random sample from N(μ, σ2). Find the Moment Generating Function of X̅. If n = 16 and σ = 2, compute P(-1 ≤ X̅ - μ ≤ 1).Let Xi be arandom sample from U(0,1)prove that Xn’ convarges in probability to 0.50