Finding the CDF of a Continuous Random Variable Y based on a function of X

• 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 setofall x-values for which $(g(X) \le y_i)$.
• Then, express the probability of this setusing the CDF of $X$, $(F_X(x))$.

Visualize PDF of a Function of RV

• Let $X$ be a Uniform random variable on [-1, 1]. Its PDF is shown in the first graph.
• Select a function to visualize: Quadratic $(Z = X^2)$ or Exponential $(Z = e^X)$.
• Three graphs will appear, the transformation function $(g(X))$, the original PDF of X, and the resulting PDF of $Z$.
• Click on the PDF of $Z$ graph to highlight a region.
• Alternatively, type a start and end value in the Highlight $Z$ Range panel to see the charts update in real-time.

Calculate PDF of a function of multiple RVs

• Two problems are provided. Use the Next and Prev buttons to switch between them.
• Press START to begin. You will be prompted to enter the value of the PDF, $(f_Z(z))$, for 5 random values of $(z)$.
• Submit each value by clicking the button or pressing Enter. Your point will be plotted on the graph.
• Once all 5 points are entered, the complete, correct PDF of $Z$ will be plotted for comparison.