Given m data records, x(1),x(2),…,x(m), each with n features, x1,x2,..xn , and m corresponding target output values, y(1),y(2),…y(m), describe the model, cost function and optimisation techniques that are commonly used with linear regression. Mathematical equations are not required for the optimisation techniques but should be included for the model and cost function.
Given m data records, x(1),x(2),…,x(m), each with n features, x1,x2,..xn , and m corresponding target output...
The independent random variables X1, X2, ... Xn are each uniformly distributed on (0,1). M is the minimum number of X's that sum to a value of at least one. (so if X1 = .4, X2, = .5, and X3 = .3, M would be 3 since 3 X values were needed for the sum of all the X's to be at least 1). a. What is the probability mass function of M. b. What is the expected value of...
9 Let Xi, X2, ..., Xn be an independent trials process with normal density of mean 1 and variance 2. Find the moment generating function for (a) X (b) S2 =X1 + X2 . (c) Sn=X1+X2 + . . . + Xn. (d) An -Sn/n 9 Let Xi, X2, ..., Xn be an independent trials process with normal density of mean 1 and variance 2. Find the moment generating function for (a) X (b) S2 =X1 + X2 . (c)...
A firm uses two inputs x1 and x2 to produce output y. The production function is given by f(x1, x2) = p min{2x1, x2}. The price of input 1 is 1 and the price of input 2 is 2. The price of output is 10. 4. A firm uses two inputs 21 and 22 to produce output y. The production function is given by f(x1, x2) = V min{2x1, x2}. The price of input 1 is 1 and the price...
2. Suppose that X1, X2, ..., Xn " N(41,01) and Yı,Y2,...,Ym * N(H2;02) are two independent random samples. (a) What is E[X - Ÿ]? (b) Find a general expression for Var[X – Ý), and use this to find an expression for the standard error ox-ý = StDev(X – Ỹ). (c) Suppose that of = 2 and o = 2.5, and also that n = 10 and m = 15. Determine the probability P(|X – Ý - (µ1 – 42)| <...
Consider the following network: 01-0 W11-1 W13-5 x,-1 W03-0 X2 2 W22-1 Obtain the output Y for the following cases: (a) All the neurons are represented by a linear function with slope of 1 (y-x) (b) All the neurons are represented by a McCulloch-Pitts model (hard limit activation function with negative threshold zero) (c) All the neurons are represented based on a sigmoid activation function. Consider the following network: 01-0 W11-1 W13-5 x,-1 W03-0 X2 2 W22-1 Obtain the output...
Question 2 (a) Determine whether the discrete time system which has an output y[n] 2*x[n] over the nterval 010 is linear or not by determining the response yi[n] to the input signalxj[n]- sin( (2*pi / 10 ) * n ) and the response y2[n] to the input signal x2[n] = cos( (2*pi/10 ) * n ). Determine the response y3[n] to the input signal x1n] = xi [n] + x2[n] and compare it with y4[n] = [n] + y2[n] ....
Consider X1,X2, , Xn be an iid random sample fron Unif(0.0). Let θ = (끄+1) Y where Y = max(X1, x. . . . , X.). It can be easily shown that the cdf of Y is h(y) = Prp.SH-()" 1. Prove that Y is a biased estimator of θ and write down the expression of the bias 2. Prove that θ is an unbiased estimator of θ. 3. Determine and write down the cdf of 0 4. Discuss why...
2-If X1(z)Find the Z-Transform of X2[x]-X, ln +3]u[n] Find theZ-Transform of X211 ( I-hind the Inverse Z-transform of given function. a) R(Z) =- (1-e") (-(z-e-ar) 3 +282+8-1 b) F (Z) = (2-2)2(2+2) Find the Z-Transform of X2 [x] = X1 [n + 3] u [n] 3- Solve the difference equation 3 4 With initial conditions y-1] 1 and yl-2] 3 4- Let the step response of a linear, time-invariant, causal system be 72 3) ulnl 15 3 a) Find the...
Format L 01 X ✓ fx K L M N C X2 15 Question 14: Note that Y represents the dependent variable and X1-X3 represent 3 (quantitative) independent variables. Let a=0.05. A Y 155 168 147 192 134 152 B X1 99.43 99.67 97.95 99.97 97.16 98.62 97.32 97.99 98.79 99.26 99.63 97.86 98.97 97.81 99.23 D X3 0.56 0.62 0.49 0.75 0.29 0.51 0.13 0.48 0.62 0.68 0.71 0.19 0.62 0.27 (a) Write out the estimated regression line (including...
Consider a multiple regression model of the dependent variable y on independent variables x1, X2, X3, and x4: Using data with n 60 observations for each of the variables, a student obtains the following estimated regression equation for the model given: y0.35 0.58x1 + 0.45x2-0.25x3 - 0.10x4 He would like to conduct significance tests for a multiple regression relationship. He uses the F test to determine whether a significant relationship exists between the dependent variable and He uses the t...