An ecologist wishes to mark off a circular sampling region having radius 11 m. However, the radius of the resulting region is actually a random variable R with the following pdf. -- (11 - n²] 3 10
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![An ecologist wishes to mark off a circular sampling region having radius 11 m. However, the radius of the resulting region is actually a
random variable R with the following pdf.
(11 – 1y2]
-
10 <rs 12
f(r) =
otherwise
What is the expected area of the resulting circular region? (Round your answer to two decimal places.)
m2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F638e261a-c42c-46ef-873a-8e2d39442a11%2Fb6ff72a6-08c6-4ca4-bc5e-46c15de1f351%2Fl52cn8_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
