The mobility of an insect is an important part of its survival. Researchers have determined that the probability that a marked flea beetle, Phyllotreta cruciferae or Phyllotreta striolata, will be recaptured within a certain distance and time after release can be calculated from the probability density function

where t is the time after release (in hours), x is the distance (in meters) from the release point that recaptures occur, L is the maximum distance from the release point that recaptures can occur, and D is the diffusion coefficient.

(a) If t = 12, L = 6, and D = 38.3, find the probability that a flea beetle will be recaptured within 3 m of the release point.
(b) Using the same values for t, L, and D, find the probability that a flea beetle will be recaptured between 1 and 5 m of the release point.

Transcribed Image Text:

p(x, t) = e-x²/(4D1) e-u²1 (4Dt) du -L Jo