Answer: 3.0

## Solution First, we need to find the value of C. Since this is a probability density function, the sum of all probabilities must equal 1: $$C = 1 - 0.15 - 0.25 - 0.35 = 0.25$$ Now we have the complete probability distribution: - P(X=1) = 0.15 - P(X=2) = 0.25 - P(X=3) = 0.35 - P(X=4) = 0.25 The **mode** is the value with the highest probability in the distribution. Comparing the probabilities: - P(X=1) = 0.15 - P(X=2) = 0.25 - P(X=3) = 0.35 (highest) - P(X=4) = 0.25 Therefore, the mode is **x = 3**, which corresponds to option D. **Key Concept**: The mode of a probability distribution is the value that occurs with the highest probability.

Author: Tanishq Prabhu