Tasks

Calculate the CDF of a Function of a Random Variable

Instructions
  • A graph of \(Y = g(X)\) is shown, and a random point \(y_i\) is chosen on the y-axis.
  • Your goal is to construct the formula for the CDF of Y at that point, \(F_Y(y_i) = P(Y \le y_i)\).
  • First, find the set of all x-values for which \(g(X) \le y_i\).
  • Then, express the probability of this set using the CDF of X, \(F_X(x)\).
  • Click on or drag the required components from the "Available Tiles" panel into the "Your Answer" panel to build the formula.
  • Click Submit and check the Observations panel for detailed feedback.
For the given graph \(Y = g(X)\), find the formula for the CDF of \(Y\) at the point y_?.
Graph of Y = g(X)

Available Tiles

Your Answer Formula for \(F_Y(y_i)\)

Observations
Start by building the formula for the given point.