Question

Given below is the distribution of a random variable \(X\):
\[ \begin{array}{|c|c|} \hline X = x & P(X = x) \\ \hline 1 & \lambda \\ 2 & 2\lambda \\ 3 & 3\lambda \\ \hline \end{array} \] If \(\alpha = P(X<3)\) and \(\beta = P(X>2)\), then \(\alpha : \beta = \)

• A. \(\frac{2}{5}\)
• B. \(\frac{3}{4}\)
• C. \(\frac{4}{5}\)
• D. \(\frac{3}{7}\)

Hint:

The probability ratio between events is determined by comparing their individual probabilities.

Answer 1

The Correct Option is D

For a distribution of random variable \(x\): \[ \alpha = P(X<3) = P(X = 1) + P(X = 2) = \lambda + 2\lambda = 3\lambda \] \[ \beta = P(X>2) = P(X = 3) = 3\lambda \] Hence, \(\alpha : \beta = 3 : 7\).