Answer to Question #340501 in Statistics and Probability for sezi

Question

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

𝑓𝑥(𝑥) = {𝑐 (1 −(1/16) 𝑥*2 , 0 < 𝑥 < 2

0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒}

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 𝑐 that makes 𝑓𝑥(𝑥) a valid probability density function.

b. 𝑃(0.1 < 𝑋 < 0.4).

c. 𝐸(𝑋) and 𝑉𝑎𝑟(X)

Answer 1

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