Question-93

Conditional Probability

Let \(X\) be a random variable such that \(P(X = 1) = k, P(X = 2) = 2k, P(X = 3) = P(X = 4) = k^2, P(X = 5) = 2k^2\). What is the value of \(P(1<X<4 \hspace{0.5mm}|\hspace{0.5mm} X>2)\)? Enter your answer correct to 2 decimal places.

Find the value of \(k\) by using the property of being valid PMF which is \(\sum_{i=1}^{n}P(X = x_i) = 1\).

0.25