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Consider the following cumulative distribution function (cdf) F X (x)=C(1−e −⁽ˣ/λ⁾ᵏ ) defined for x≥0,k>0, and λ>0. I.

What is the value of C ?

User Alexloehr
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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.

User Contra
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