Aparabolic satellite dish reflects signals to the dish’s focal point. an antenna designer analyzed signals transmitted to a satellite dish and obtained the probability density function f(x) = c(1 - 1/16x^2) for 0 < x < 3, where x is the distance (in meters) from the centroid of the dish surface to a reflection point at which a signal arrives. determine the value of c that makes f(x) a valid probability density function

Step-by-step explanation:

The probability density function is :

With 0 < x < 3

To be a valid probability density function :

Where a < x < b

And also

f(x) ≥ 0 for a < x < b

Applying this to the probability density function of the exercise :

We can verify by replacing ''c'' in the original probability density function and integrating :

Also, f(x) ≥ 0 for 0 < x < 3

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step-by-step explanation:

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