Find a constant k so that kf is a probability density function, or state it does not exist.
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C) k = 6
D) does not exist

Question

Find a constant k so that kf is a probability density function, or state it does not exist.
-
C) k = 6 
D) does not exist

Quizplus · Accepted Answer

For a probability density function, the area under the curve must be equal to 1. Thus, we need to find a constant k that makes the integral of kf equal to 1 over its support.

If we assume that f is a continuous uniform distribution on the interval [1,3], then we have:

∫1^3 kf dx = k ∫1^3 f dx = k [x]1^3 = k(3-1) = 2k

Thus, we need to solve for k such that 2k = 1. This gives us k = 1/2.

Therefore, kf is a probability density function with k = 1/2.

Find a Constant K So That Kf Is a Probability