A parabolic 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 - 16¹²) for 0 < x < 1, 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 following: (Round your answers to two decimal places (e.g. 98.76).) (a) Value of c that makes f(x) a valid probability density function c = i (b) P(X ≤ 0.4) = (c) P(0.1 < X < 0.4) =

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