Recent content by stukbv

Sorry, I just want to know why they're true, they are in my lecture notes and I can't work out why we know these inequalities hold.

Hello, could somebody please explain to me how 1-exp(-μt) ≤ μt and similarly (1-exp(-μt))exp(-λt) ≥ μt-μ2t2\2)(1-λt) Thanks a lot

Homework Statement Take f: (a,b) --> R , continuous for all x0in (a,b) and take (Ω = (a,b) , F = ( (a,b) \bigcap B(R)) where B(R) is the borel sigma algebra Then prove f is a borel function The Attempt at a Solution I know that continuity of f means that for all x in (a,b) and all...

So I have a definition; Xn n=1,2... is a sequence of random variables on ( Ω,F,P) a probability space, and let X be another random variable. We say Xn converges to X almost surely (P-a-s) iff P({limn →∞ Xn=X}C) = 0 It then goes on to say that checking this is the same as checking limm...

I see, thata makes sense. Thanks for your help

My lecturer has said that beppo levi means for and increasing sequence of Xi where Xi is simple for all i, it holds that ∫limi → ∞XidP = limi → ∞∫XidP But why is it that he later says things like ∫ limi→ ∞ Ʃin=1P2(Bw1n)dP1(w1) = limi → ∞Ʃin=1∫P2(Bw1n)dP1(w1) is a result of beppo...

Ok, but I can't find them because I don't know what I'm looking for.. I don't understand what it means by let x be some additional given value of the explanatory variable. I mean, does this mean we have n+1 explanatory variables x1,x2...xn,x so that Y = α + β(x-xbar) + σε is the response...

βHomework Statement Data y1,y2...yn are modeled as observations of random variables Y1,..Yn given by Yi = α + β(xi-xbar) + σεi Where α , β and σ are unknown parameters x1,x2...xn are known constants and xbar is (1/n)Ʃxi and εi's are independent random variables each with the...

I see thamk you!

I know that you differentiate to get the density function but I can't work out whether its with respect to theta (which is what I did above) or with respect to m?

Homework Statement (x1,x2,...xn) is modeled as observed values of independent random variables X1,X2,...Xn each with the distribution 1/θ for x in [0,θ] and 0 otherwise. A proposed estimate of θ is m = max(x1,...xn) Calculate the distribution of the random variable M=max(X1,X2,...Xn) and...

Homework Statement I am told that I have particles which each yield a random number of offspring of known distribution independently from each other and from the past generations. Xn is the number of particles in the nth generation The distribution of a typical family size is Z and so...

I think my lecturer wants me to do it this way. So y must be between - infinity and 0? Is my pdf correct now?

Homework Statement I am told that X is a random variable with uniform distribution over [0,1] I need to find the mean and variance of log(X) 2. The attempt at a solution I assume I must find the pdf of log(X) so I did this as follows; Let Y=log(X) Then to find the cumulative...

Homework Statement I have a Stochastic Processes test coming up soon and we are taught about the first passage decomposition. I understand this but it then says that it changes it to a generating function Homework Equations Generating function Pij(s) = Ʃ pij(n)sn...