Exercise 4. A certain species of plant always has either three or five leaves. The number is random, with P(3 leaves) = 0.4 and P(5 leaves) = 0.6. Each plant has a flower which, randomly, is either open or closed, with probabilities P(open) = 0.8 and P(closed) = 0.2. A botanist collects 1000 randomly chosen plants from this species and finds the following distribution of traits: open 3 leaves N3,open 5 leaves N5,open closed N3, closed N5,closed a) Assuming the two traits are independent, determine the expectations of the counts N3,open, N3,closed, N5,open, and N5,closed in the table. b) Determine an approximate value for the probability P(N3,open > 340).
Exercise 4. A certain species of plant always has either three or five leaves. The number is random, with P(3 leaves) = 0.4 and P(5 leaves) = 0.6. Each plant has a flower which, randomly, is either open or closed, with probabilities P(open) = 0.8 and P(closed) = 0.2. A botanist collects 1000 randomly chosen plants from this species and finds the following distribution of traits: open 3 leaves N3,open 5 leaves N5,open closed N3, closed N5,closed a) Assuming the two traits are independent, determine the expectations of the counts N3,open, N3,closed, N5,open, and N5,closed in the table. b) Determine an approximate value for the probability P(N3,open > 340).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Exercise 4. A certain species of plant always has either three or five leaves. The number is
random, with P(3 leaves) = 0.4 and P(5 leaves) = 0.6. Each plant has a flower which, randomly,
is either open or closed, with probabilities P(open) = 0.8 and P(closed) = 0.2. A botanist collects
1000 randomly chosen plants from this species and finds the following distribution of traits:
open
3 leaves N3,open
5 leaves
N5,open
closed
N3,closed
N5, closed
a) Assuming the two traits are independent, determine the expectations of the counts №3,open,
N3, closed, N5,open, and N5,closed in the table.
b) Determine an approximate value for the probability P(N3,0pen > 340).
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