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1. Riemann Integrability

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...
2. Markov Chain

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...
3. Convolution and Probability Distributions

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 =...
4. Real Analysis - Mean Value Theorem Application

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...
5. Wien's Law

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...