Question

The probability density \( f(x) \) of a continuous random variable is given by \( f(x) = K e^{-|x|} \) for \( -\infty < x < \infty \). Then the value of \( K \) is:

• A. \( \frac{1}{2} \)
• B. 2
• C. 1
• D. 4

Hint:

For probability density functions, always ensure that the integral of the function over the entire range is equal to 1. This helps in finding the normalization constant.

Answer 1

The Correct Option is A

Step 1: Use the normalization condition. The total probability for a continuous random variable must equal 1, so we normalize the probability density function by integrating over its entire range and solving for \( K \).
Step 2: Conclusion. Thus, the value of \( K \) is \( \frac{1}{2} \).