Biologists are observing grunion run on a 4- mile long stretch of beach (the starting point is labeled 0 mi & the ending point labeled 2 mi, similar to a number line or a ruler). Assuming that the run happens on any point on this stretch with equal probability, let the continuous random variable X be the location of the run, then the probability distribution (or density) of X is p(x) = ¼ for 0≤x≤4 p(x) = 0 otherwise (x<0 or x>4) (Hint: Sketch the graph y=p(x)) Calculate: (a) Justify the model above (b) Pr ( 0 mi < X < ¼ mi) – hint: find the enclosed area (c) Pr ( ¼ mi < X < ½ mi ) (d) Pr ( ¼ mi < X < ¾ mi ) (e) Pr ( 1 mi < X < 2 mi )
Biologists are observing grunion run on a 4-
mile long stretch of beach (the starting point is
labeled 0 mi & the ending point labeled 2 mi,
similar to a number line or a ruler). Assuming
that the run happens on any point on this
stretch with equal probability, let the
continuous random variable X be the location
of the run, then the probability distribution (or
density) of X is
p(x) = ¼ for 0≤x≤4
p(x) = 0 otherwise (x<0 or x>4)
(Hint: Sketch the graph y=p(x)) Calculate:
(a) Justify the model above
(b) Pr ( 0 mi < X < ¼ mi) – hint: find the
enclosed area
(c) Pr ( ¼ mi < X < ½ mi )
(d) Pr ( ¼ mi < X < ¾ mi )
(e) Pr ( 1 mi < X < 2 mi )
(f) If there aren’t enough observers to monitor
the entire 4-mi stretch, determine the
length of beach that needs to be monitored
so that there is at least a 75% probability
the team will be observing the grunion run
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