(2) For arbitrary function f(q, p,1), show that a d dq; dt - dô dt aH | 5 (9, p. 1) = {1, 841}}
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by Bartleby Expert- Consider a 6-meter metal bar with a uniform initial temperature (across the bar) of 35°C . Suppose it is in thermal contact with an external source of heat given by h(x)= 3−x, 0 ≤ x ≤ 6. So the temperature u(x,t) had the ut=uxx+h(x) permission. Suppose further that the temperature of the ends are kept constant, being at x=0 of 5°C , while at x=6 of 30°C . Under such conditions: Find the steady-state temperature distribution of the bar and the boundary value problem that determines the transient distribution. (no need to solve the problem).A rectangular plate with insulated surface is 10 cm. wide and so long compared to its width that it may be considered infinite length. If the temperature along short edge y = 0 is given u(x,0) = 8 sin(px/ 10) when 0 <x <10, while the two long edges x = 0 and x = 10 as well as the other short edge are kept at 0o C, find the steady state temperature distribution u(x,y).f X1,X2,...,Xn constitute a random sample of size n from a geometric population, show that Y = X1 + X2 + ···+ Xn is a sufficient estimator of the parameter θ.
- 4. The table shows data on the number of visitors to the Malaysia in a month, v (1000s), and the amount of money they spent, m (MYR millions), for each of 8 months (CO2, C3, PO1) Number of visitors, 2450 2480 2540 2420 2350 2290 2400 2460 v (1000s) Amount of money spent, 1370 1350 1400 1330 1270 1210 1330 1350 m (MYR millions) a) Solve product moment correlation coefficient between v and m. b) Describe the reason to support fitting a regression model of the form m = Bo + Biv to these data c) Find the value of ß; correct to 3 decimal places d) Illustrate the equation of the regression line of m on v e) Interpret your value of ß; f) Use your answer to part (d) to estimate the amount of money spent when the number of visitors to Malaysia in a month is 2,500,000 g) Comment on the reliability of your estimate in part (f). Give your reason.If X is exponentially distributed with parameter λ and Y is uniformly distributed on the interval [a, b], what is the moment generating function of X + 2Y ?Consider the geometric Brownian motion with σ = 1: dS = μSdt + SdX, and consider the function F(S) = A + BSα. Find any necessary conditions on A, B, and α such that the function F(S) follows a stochastic process with no drift.
- Assume an asset price S_t follows the geometric Brownian motion, dS_t = µS_tdt + σS_dW_t, where µ and σ are constants and r is the risk-free rate. 1. Using the Ito’s Lemma find the stochastic differential equation satisfied by the process Xt = S_t^n , where n is a constant. 2. Compute E[X_t] and Var[X_t]. 3. Using the Ito’s Lemma find the stochastic differential equation satisfied by the process Y_t = S_tertLet X1 ... Xn i.i.d random variables with Xi ~ U(0,1). Find the pdf of Q = X1, X2, ... ,Xn. Note that first that -log(Xi) follows exponential distribuition.Suppose that f(x,y)∈C^2 in some neighborhood of (a,b) and that fx(a,b)=0=fy(a,b). If the Hessian matrix of f is (3−3−3−5) at a critical point (a,b), then (a,b) is a saddle point local minimum local maximum degenerate critical point
- State the solution formula for the Cauchy problem for the homogeneous wave equation on R3. Prove that solutions corresponding to a localized initial signal (i.e. initial position and derivative are supported in a small ball) have a wave fore front and a wave back front and that these fronts are close to each other. Conclude that music is possible in R3. Say in words what happens if we consider R2 instead.31 - Find the regression model. Regresyon modelini bulunuz. Y X 2 5 5 9 7 4 4 11A) y=-3,21+2,11xB) y=2,56+5,43xC) y=5,27+0,11xSuppose we have collected a random sample from our population, denoted by (xi , yi), i = 1, . . . , n. We now fit a least squares line: yˆi = βˆ 0 + βˆ 1xi (i = 1, . . . , n). What additional assumption do we need in order to carry out statistical inference on our least square estimators βˆ 0 and βˆ 1? c. Using the results we’ve derived in class, prove that the sum of residuals is zero (Pn i=1 ei = 0)