Recent content by Mark53

##X^TX## That would be a square matrix, which means it has an inverse

##XA{(A^TX^TXA)^-}^1A^TX^T## ##=XA{A^-}^1{X^-}^1{(X^T)^-}^1{(A^T)^-}^1A^TX^T## ##=XI{X^-}^1{(X^T)^-}^1({A^-}^1A)^TX^T## ##=X{(X^TX)^-}^1IX^T## ##=X{(X^TX)^-}^1X^T## Is this correct now?

We know that A is invertible which means we can: $$XA{A^-}^1{(A^TX^TXA)^-}^1A^TX^T$$ $$=X{(A^TX^TXA)^-}^1A^TX^T$$

Wait would it be $$(X^*)^T = (XA)^T= A^TX^T$$ which would give$$XA{(A^TX^TXA)^-}^1A^TX^T$$ Where would I go from here?

Homework Statement given that X is an n × p matrix with linearly independent columns. And $$X^∗ = XA$$ where A is an invertible p × p matrix. a) Show that: $$X^*{({X^*}^TX^*)^-}^1{X^*}^T = X{(X^TX)^-}^1X^T$$ b) Consider two alternative models $$M : Y = Xβ + ε$$ and $$M^∗ : Y = X^∗β ^∗ +...

Homework Statement Define a simple random walk Yn on a finite state space S = {0, 1, 2, . . . , N} to be a random process that • increases by 1, when possible, with probability p, • decreases by 1, when possible, with probability 1 − p, and • remains unchanged otherwise. (a) Specify the...

its a probability course and I have heard of the birth-death process SIS means going from susceptible to the disease to being infected to returning to being susceptible given that 1 individual is already infected the state space must be 1 to 50

A Health company would like to see how a disease will spread if one infected individual was to arrive in a country with a population of 50 people. The diseases is known to follow SIS (susceptible-infected-susceptible) dynamics with the following probabilities The number of infected...

when multiplying the state space by the transition matrix How would I know if the individual is infected or not?

Homework Statement [/B] The population is 50 The diseases is known to follow SIS dynamics with the following probabilities The number of infected individuals increases with probability 0.1 and it decreases with probability 0.05 the probability that nothing happens is 0.85 a) what is the...

Do I need to see if the series converges or find the partial sum? not sure how to start solving it

when calculating the sum I get: the sum of x=0 to ∞ of (e^tx)/(2^x)=e^t/2 which is wrong am I still missing something?

Homework Statement [/B] Let X be a random variable with support on the positive integers (1, 2, 3, . . .) and PMF f(x) = C2 ^(-x) . (a) For what value(s) of C is f a valid PMF? (b) Show that the moment generating function of X is m(t) = Ce^t/(2− e^t) , and determine the interval for t for...

thanks for the help!

P(x<1)*P(x<1) (1-e^(-1))*(1-e^(-1)) =1-2e^(-1)+e^(-2) =0.3996