Var(∑AiYi): Calculating & Explaining the Formula

Context: Graduate
Thread starter milk
Start date Apr 18, 2006

Join the discussion

Registration is free. Ask a follow-up in this thread, or start your own.

1 reply · 3K views

milk

Thread starter
Apr 18, 2006

Var( ∑AiYi)= ∑(Ai^2) Var(Yi)
Could you show why?
Thank you

Physics news on Phys.org

Twisted laser light distinguishes mirror-image molecules by their fragment counts
A quantum heat engine that simultaneously provides work and refrigeration
Long-lived ytterbium states could sharpen quantum computing and atomic clocks

mathman

Science Advisor

Homework Helper

Apr 19, 2006

Your equation includes an assumption that the Y's are independent random variables. In this case, you only need to show it for one variable, i.e. var(AX)=A²var(X). This then can be shown by using the definition of var in terms of first and second moments.

Var(∑AiYi): Calculating & Explaining the Formula

Graduate Expected numbers of cards of a last color remaining

Graduate Probability puzzle

Undergrad The problem of points

Undergrad The countability paradox of computable numbers

Undergrad How does axiom of foundation prevent infinite sequence of elements?

Insights Revisiting the Velocity-Time Function

Insights Remote Operated Gate Control System

Insights AI Enriched Problem Solving

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Var(∑AiYi): Calculating & Explaining the Formula

Similar threads