Advanced Mathematics

1. The effectiveness of some solar energy heating units depends on the amount of radiation available from the sun. During a typical October, daily total solar radiation in Tampa, Florida, approximately follows the following probability density function (units are hundreds of calories): Ax) = { 3 32 (x- 2)(6 - x) 2 <xs 6 0 elsewhere

a) Find the cumulative distribution function.

b) Find the probability that solar radiation exceeds 300 calories on atypical October day.

c) What amount of solar radiation is exceeded on exactly 50% of the

d) Find the expected daily radiation for October.



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