Homework Statement
Prove or give a counter example of the following statement:
If f: [a,b] \to [c,d] is linear and g:[c,d] \to \mathbb{R} is Riemann integrable then g \circ f is Riemann integrable
Homework Equations
The Attempt at a Solution
I'm going to attempt to prove the statement...
Homework Statement
-A bus is moving along an infinite route and has stops at n = 0, 1, 2, 3, ......
-The bus can hold up to B people
-The number of people waiting at stop n, Yn, is distributed Poisson(10) and is independent from the number waiting at all the other stops.
-At any given stop each...
Homework Statement
Have 2 iid random variables following the distribution f(x) = \frac{\lambda}{2}e^{-\lambda |x|}, x \in\mathbb{R}
I'm asked to solve for E[X_1 + X_2 | X_1 < X_2]
Homework Equations
The Attempt at a Solution
So what I'm trying to do is create a new random variable Z =...
Homework Statement
Let f: R -> R be a function such that \lim_{z\to 0^+} zf(z) \gt 0 Prove that there is no function g(x) such that g'(x) = f(x) for all x in R.
Homework Equations
Supposed to use the mean value theorem. If f(x) is continuous on [a,b] and differentiable on (a,b) then...
Hi,
I'm supposed to prove that Wien's Law: P(\lambda,T) = \frac{f(\lambda T)}{\lambda^5} includes Stefan-Botlzmann's Law R(T) = \sigma T^4 and Wien's Displacement Law: \lambda_{max} T = b
For Wien's Displacement Law:
I know that I would have to find when P(\lambda ,T) graphed against...