Nneetquant
Get started

Normalizing a tilted density

EasyRandom VariablesCalculus~3m

A density has the form f(x)=c(1+x)f(x) = c(1+x) on [0,1][0,1] and 00 elsewhere. After finding the constant cc, compute P(X>12)P\big(X > \tfrac12\big). (to 4 decimals)

Show hints (2)+
  1. First normalize: ∫₀¹ c(1+x) dx = 1 gives c = 2/3.
  2. Then P(X>12)=∫1/2123(1+x) dx=712P(X>\tfrac12) = \int_{1/2}^1 \tfrac23(1+x)\,dx = \tfrac{7}{12}.

Answer

Reveal answer →

0.5833 (± 0.0005)

Want the full step-by-step worked solution? It's part of Premium - along with a worked solution for every question in the bank.

Practise freeUnlock solutions

Asked at: Timed Mental-Math & Sequences, Game-Based Aptitude

Related questions