Tasks

Cumulative Distribution Function (CDF)

Instructions
    Procedure:
    • Click the button to generate a random number "c".
    • Find the inverse image from \(X \leq c\) for the given RV \(X\) by selecting the correct set. The system will check your answer immediately.
    • If your inverse image is correct, calculate and enter the CDF value, \(F_X(c)\).
    • Click "Submit" to check your final answer.

Given \(\Omega = \{\omega_1, \omega_2, \omega_3, \omega_4\}\), a probability measure where \(P(\{\omega_1\}) = 0.2\) and \(P(\{\omega_2,\omega_3,\omega_4\}) = 0.8\), and a Random Variable \(X\) defined as: \(X(\omega_1) = 1\), \(X(\omega_2) = 2\), \(X(\omega_3) = 2\), \(X(\omega_4) = 2\).

1. Find the inverse image, which is the set \(\{\omega \in \Omega : X(\omega) \le c\}\)

\(\phi\)
\(\{\omega_1\}\)
\(\{\omega_2, \omega_3, \omega_4\}\)
\(\{\omega_1, \omega_2, \omega_3, \omega_4\}\)

2. Now, find \(F_X(c) = P(\{\omega \in \Omega : X(\omega) \le c\})\)

Observations