Problem: The cdf function

Problem

\(X\) is a random variable with cumulative distribution function \(F\) .

  1. Is it possible that \(F\left( 2 \right)>F(3)\) ?
  2. Is it necessary that \(F\left( 2 \right)<F(3)\) ?
  3. Is it necessary that \(F\left( 2 \right)≤F(3)\) ?
  4. If \(a<b\) is it then necessarily true that \(F\left( a \right)≤F(b)\) ?
  5. Is \(F\) necessarily an increasing function?

Solution