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.