Tasks
Instructions
    Quick theory overview:
    • Here, we want to find the CDF of a random variable \(X\) at a randomly generated value "c" by finding the inverse image which we learnt in the previous experiment and using the given probability measure.
      • Procedure:
    • Click on the button to generate a random number "c".
    • Find the inverse image of the generated random number "c" for the given random variable \(X\) and select the appropriate inverse image.
    • Based on the inverse image calculated and the probabiliy measure given, find the CDF of the random variable \(X\) at "c" and enter the value in the input box.
    • Click on the "Submit" button to check your answer.
    • Click on the "Reset" button to reset the experiment.


Given a sample space \(\Omega = \{\omega_1,\omega_2,\omega_3,\omega_4\}\) , event space \(\mathcal{F}\) = \(\{\phi,\{\omega_1,\omega_2,\omega_3,\omega_4\},\{\omega_1\},\{\omega_2,\omega_3,\omega_4\}\}\) , a probability measure \(P\) such that \(P(\{\omega_1\}) = 0.2\), \(P(\{\omega_2,\omega_3,\omega_4\}) = 0.8\) , and a random variable \( X\) such that \(X(\omega_1) = 1\), \(X(\omega_2) = 2\), \(X(\omega_3) = 2\), and \(X(\omega_4) = 2.\) Find the inverse cdf of a randomly generated value for \(X\).


Find the inverse image of c for the given RV \(X\).
\(\phi\)
\(\{\omega_1\}\)
\(\{\omega_2\}\)
\(\{\omega_3\}\)
\(\{\omega_4\}\)
\(\{\omega_1, \omega_2\}\)
\(\{\omega_1, \omega_3\}\)
\(\{\omega_1, \omega_4\}\)
\(\{\omega_2, \omega_3\}\)
\(\{\omega_2, \omega_4\}\)
\(\{\omega_3, \omega_4\}\)
\(\{\omega_1, \omega_2, \omega_3\}\)
\(\{\omega_1, \omega_2, \omega_4\}\)
\(\{\omega_1, \omega_3, \omega_4\}\)
\(\{\omega_2, \omega_3, \omega_4\}\)
\(\{\omega_1, \omega_2, \omega_3, \omega_4\}\)

Now, find the CDF of the random variable \(X\) at c using this inverse image and the given probability measure.

Observations
Observation
Result