# identically

1. ### Five identically sized regular tetrahedra ....

Hi, got an answer to a question but think I may have simplified it way too much. Question is "five identically sized regular tetrahedra are denoted by j=1,2,3,4,5. Tetrahedra j is coloured blue on 5 - j sides and green on the other j - 1 sides. Part (a) asks "a tetrahedron is chosen at...
2. ### Is this identically zero?

Is x\ln x identically zero at x=0, or does it have a singularity? EDIT: silly me. I didn't mean to write 'z' there, just been doing too much complex analysis recently and got into the habit of writing z everywhere. Sorry for the confusion!
3. ### Proving a function is identically zero

If f is a continuous function on [a,b] such that \int_{a}^{b}fg = 0 for all continuous functions g. Then f=0 on [a,b]. So yeah, I know I have to invoke that U(fg)=L(fg)=0 but after that I'm stumped. Thanks.
4. ### Independent and identically distributed Random Variables

Let X1, X2,....,Xn be i.i.d random variables with pdf as: f(xi)={ 1/β 0<xi<β 0 otherwise Find the pdf of U=max{X1, X2,....,Xn}
5. ### independent identically distributed R. V's

If {X_i} for i=1,...n are i.i.d, then can we show that {X_i ^2} for i=1,..n are also i.i.d?
6. ### Prove that function is identically zero?

Let f(x) be a continuous function in [-1, 1] and satisfies 2f(2x^2 - 1) = 2x\cdot f(x)\ \forall\ x\in [-1, 1]. Prove that f(x) is identically zero \forall\ x\in [-1, 1].
7. ### Two independant and identically distributed uniform distributions

Let U and V be independent and identically distributed uniformly on the interval [0, 1]. Show that for 0<x<1; P(x<V<U^2)=1/3 - x + (2/3)*x^3 and hence write down the density of V conditional on the event that V<U^2.
8. ### independently and identically distributed random variables

Hi there, Assume that Y1, Y2, Y3 and Y4 are independently and identically distributed N(\mu, \sigma^2) random variables. how do I show that Y1 + Y2 - Y3 - Y4 and Y1 - Y2 + Y3 - Y4 are independent. Thanks Casper