Recent content by WantToBeSmart

Solved (for the median and I omit c): Pr(Y>y_M)=0.5=Pr(X>x_M)\\ Pr(aX^b>y_M)=0.5\\ Pr\left[X>\left(\frac{y_M}{a}\right)^b\right]=0.5 It is true for any percentile of the distribution, just need to replace 0.5 and y_M with appropriate expressions.

I am dealing with a random variable which is a transformation of another random variable of the form: Y:=aX^b+c The pdf of the random variable X is known and for the sake of example let it be exponential distribution or any other distribution with known and commonly available quantile...

Homework Statement I need to prove that a 4x4 matrix has 2 zero eignenvalues. 2. The attempt at a solution I have tried to obtain the characteristic equation but calculating the determinant of a relevant 4x4 is rather daunting as there aren't many zeros. I was wondering if there is...

I am struggling to understand the concept of natural parametrization of pdf of exponential family. Say that we have a function with the following pdf: f(x;\theta)=exp\left[\sum_{j=1}^k A_j(\theta)B_j(x)+C(x)+D(\theta)\right] where A and D are functions of \theta alone and B and C are functions...

Hi Sammy, I know the definition of e but the limit is still not trivial to me. Is the equation below some sort of a rule? Thanks! lim_{k\to\infty}(1+\frac{b}{k})^k= e^b You're right. I added ^2

Homework Statement I'm trying to prove that the random variable with t distribution with k degrees of freedom will have N(0,1) as k→∞ the two equations below are derived from the pdf of the t-distribution: 2. Homework Equations which I can't get my head around...

Hey, it is going to be chi-squared distirbution with 1 degree of freedom. By definition of chi-squared. The mean follows from there as well.

Checked that and it was another mistake I was making. Thank you for pointing this out!

I think it definitely solves this problem! Now I can proceed with the rest of the exercise. Thank you Robert!

Hey, I have a pdf of a random variable Z given. I am being asked to calculate what the moment generating function of a r.v Y= Z + c will be where c is a constant in ℝ I tried to calculate it in the following way: \int^∞_0 e^{(z+c)t} f(z+c)dz where f(z) is an exponential pdf with...