Question

A random variable \(X\) has the following pdf:
\[ f(x) = \frac{1}{\sqrt{12\pi}} e^{-\frac{(x-1)^2}{6}}; \quad -\infty < x < \infty \]
\(= 0\), otherwise.
Then \(\int_{1}^{\infty} f(x)dx = ?\)

• A. 0
• B. \(\frac{1}{2}\)
• C. \(1 - \frac{1}{e}\)
• D. 1

Hint:

For any normal distribution, the probability of obtaining a value greater than the mean is always exactly 0.5.
Once you identify that the lower limit of integration is the mean of the distribution, you can write the answer \(\frac{1}{2}\) immediately without performing any integration.

Answer 1

The Correct Option is B