The pressure X, measured in psi (pound-force per square inch), at the wings of a turbine that is tested in a tunnel, follows the so-called Rayleigh distribution with density function

where a = 1∕20 000 and c is a positive constant.
(i) What is the value of c?
(ii) Find the distribution function of X and use it to calculate the probabilities that the value of the pressure

(a) is at most 200 psi;

(b) is between 100 and 200 psi.
(iii) If it is known that, at a certain instant, the value of the pressure exceeds 100 psi, what is the probability that it has not exceeded twice that value?

Transcribed Image Text:

f(x) = cxe-ax x > 0,