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Location of a Bee Swarm A swarm of bees is released from a certain point. The proportion of the swarm located at least 2 $\mathrm{m}$ from the point of release after 1 hour is a random variable that is exponentially distributed with $a=2$ .a. Find the expected proportion under the given conditions.b. Find the probability that fewer than 1$/ 3$ of the bees are located at least 2 $\mathrm{m}$ from the release point after 1 hour.
(a) 0.5$\qquad$ (b) 0.4866
Calculus 1 / AB
Chapter 18
Probability and Calculus
Section 3
Special Probability Density Functions
Continuous Functions
Campbell University
University of Michigan - Ann Arbor
Idaho State University
Boston College
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Okay, so for this question have gotten exponentially distributed. Random variable with lambda equals two. So our density function is as follows to eat the name too x, and we want to know the expectation. Well, expectation is just one over the lambda, which is 1/2, which is 0.5. Next. We want to know the probability that X is less than 1/3. That's going to equal the integral from zero to 1/3 of two. Need to the negative two x the X, which will be negative, eat native to X, evaluate it from 0 to 1/3 which will be one minus e to the negative 2/3 x Well, not extras. Negative 2/3. And we can get a numeric approximation for that butt. Plug it into a calculator on you should get approximately 0.486 six. So that will be one answer, and this will be our other answer up here.
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