Final answer:
The value of C in the cumulative distribution function is 1, ensuring that the total area under the probability distribution curve equals 1, as required by the properties of a probability distribution.
Step-by-step explanation:
The value of C in the given cumulative distribution function (cdf) can be found by recognizing that the total area under the curve of a probability distribution must equal 1. This is because the cumulative distribution function ultimately represents the probability that a random variable X is less than or equal to a certain value, and the total probability must sum to 1. To find C, we would set the cdf equal to 1 for the maximum value of x (which approaches infinity), solve the equation C(1 - e^{-∞}) = 1, and since e^{-∞} = 0, we get C = 1.