Convolution

Using covolution, find the solution of the differential eq y"+4y'+13y=(1/3)e^(-2t)sin3t y(0)=1, y'(0)=-2

Eigenvectors

Once you obtain eigenvalues of 8.248, 7.661, and -3.909 for the matrix 1 5 -3 5 4 2 -3 2 7 what are the next steps to obtain the eigenvectors.

Moment generating function

1. X is uniform on {1,2,3,4,5,6} m_x(s)=? m_x(s)=E(e^sX) Which is called the moment generating function of X (or the distribution of X)

Uniform distribution

1. X_1,X_2,...,X_n are independent and uniformly distributed on [0,1] a. standardize X_1+X_2+...+x_n b. Give mgf of THE STANDARDIZED (a) sum. 2. Suppose X is normal with mean u and variance sigma^2. P{u<= X <= u + 1.5 sigma}

Sum of two random variables

Z=sum of dots (uniform on {1,2,3,4,5,6} a. M_z(s)=? b. M_z(s)=M_x(s)^2 why? M_z stands for the mgf of x=sum of dots when two dice are tossed

Compute the Hypothesized Mean and then the Observed Mean of an event based on a survey. Compare these two values and calculate Statistical Significance

Tourism is one consideration for CoffeeTime's future, A survey of 1,233 visitors to mumbai last year revealed that 110 visited a small cafe during their visit. Laura claims that 10% of tourists will include a visit to a cafe. Use a 0.05 significance level to test her claim. Would it be wise for her to use that claim in tryin ...continues

Statistics

Tourism is one consideration for CoffeeTime's future, A survey of 1,233 visitors to mumbai last year revealed that 110 visited a small cafe during their visit. Laura claims that 10% of tourists will include a visit to a cafe. Use a 0.05 significance level to test her claim. Would it be wise for her to use that claim in trying ...continues

Section A - Past Exam Paper (Mathematical Methods)

I would be grateful if someone could provide me with the workings and solutions to section a of the attached paper. (parametric forms, tangent vectors, unit normal vectors of surface, vector fields, constant vectors etc)

Exam Paper - Mathematical methods

I would be grateful if someone could provide me with the workings and soulutions to QB5 of the attatched past paper. (Guass's Divergence Theorem)

Exam Paper- Mathematical methods QB6

I would be grateful if someone could provide me with the workings and soulutions to QB6 of the attatched past paper. (Stokes's Theorem)