xercise 4. A certain species of plant always has either three or five leaves. The number is ndom, with P(3 leaves) = 0.4 and P(5 leaves) = 0.6. Each plant has a flower which, randomly, either open or closed, with probabilities P(open) = 0.8 and P(closed) = 0.2. A botanist collects 00 randomly chosen plants from this species and finds the following distribution of traits: closed оpen 3 leaves| N3,0open N3,closed 5 leaves N5,0open 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
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Author:Amos Gilat
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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
closed
3 leaves N3,0pen N3,closed
5 leaves N5,0pen N5,closed
a) Assuming the two traits are independent, determine the expectations of the counts N3.open;
N3,closed, N5,open, in the table.
and N5,closed
b) Determine an approximate value for the probability P(N3,0open > 340).
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 closed 3 leaves N3,0pen N3,closed 5 leaves N5,0pen N5,closed a) Assuming the two traits are independent, determine the expectations of the counts N3.open; N3,closed, N5,open, in the table. and N5,closed b) Determine an approximate value for the probability P(N3,0open > 340).
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