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{"ops":[{"insert":"A parabolic satellite dish reflects signals to the dish\u2019s focal point. An antenna designer analyzed signals transmitted to a satellite dish and obtained the probability density function \ud835\udc53\ud835\udc65(\ud835\udc65) = { \ud835\udc50 (1 \u2212 1 \/16* \ud835\udc65*2) , 0 < \ud835\udc65 < 2; 0, \ud835\udc5c\ud835\udc61\u210e\ud835\udc52\ud835\udc5f\ud835\udc64\ud835\udc56\ud835\udc60\ud835\udc52 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: a. Value of \ud835\udc50 that makes \ud835\udc53\ud835\udc65(\ud835\udc65) a valid probability density function. b. \ud835\udc43(0.1 < \ud835\udc4b < 0.4). c. \ud835\udc38(\ud835\udc4b) and \ud835\udc49\ud835\udc4e\ud835\udc5f(\ud835\udc4b)\n"}]}
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