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 -nds the following distribution of traits: open closed 3 leaves N3,open N3,closed 5 leaves NE,open N5,closed a) Assuming the two traits are independent, determine the expectations of the counts №3,open, N3,closed, N5,0-en, and N5,close, 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 -nds the following distribution of traits: open closed 3 leaves N3,open N3,closed 5 leaves NE,open N5,closed a) Assuming the two traits are independent, determine the expectations of the counts №3,open, N3,closed, N5,0-en, and N5,close, in the table. b) Determine an approximate value for the probability P(N3,open > 340).
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
![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 nds the following distribution of traits:
open
closed
N3,closed
3 leaves N3,open
5 leaves NE,open N5, closed
a) Assuming the two traits are independent, determine the expectations of the counts №3,open,
N3,closed, N5,0-en, and N5,close in the table.
b) Determine an approximate value for the probability P(N3,open > 340).
Exercise 5. Assume that we have observed the following values from a normal distribution with
known variance o2 = and unknown mean .
1.23 -0.67 1.16 1.67 0.24 2.99 0.02 .17 0.27 21.
Test the hypothesis Ho: = 0 against the alternative H₁: #0 at significance level a = 5%.
Exercise 6. Let 0> 0 and XU[0,0], i.e. X is uniformly distributed on the interval [0,0].
a) As a function of 0, determine P(X ≤ 1).
b) Assume that is unknown, but we can observe X. For given 00, we want to test the
hypothesis H: 020 against the alternative H₁: 0 < 0o. Consider the test which rejects
Ho, if and only if X < c. .low should we choose c, as a function of 0o and a, to get a test
with significance level a? Carefully justify your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed029406-a1c1-473f-a3a0-6fd0fbd8e89d%2Fd9e169ef-df2f-4b54-8148-d6af420daf36%2Fmqgdrog_processed.jpeg&w=3840&q=75)
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 nds the following distribution of traits:
open
closed
N3,closed
3 leaves N3,open
5 leaves NE,open N5, closed
a) Assuming the two traits are independent, determine the expectations of the counts №3,open,
N3,closed, N5,0-en, and N5,close in the table.
b) Determine an approximate value for the probability P(N3,open > 340).
Exercise 5. Assume that we have observed the following values from a normal distribution with
known variance o2 = and unknown mean .
1.23 -0.67 1.16 1.67 0.24 2.99 0.02 .17 0.27 21.
Test the hypothesis Ho: = 0 against the alternative H₁: #0 at significance level a = 5%.
Exercise 6. Let 0> 0 and XU[0,0], i.e. X is uniformly distributed on the interval [0,0].
a) As a function of 0, determine P(X ≤ 1).
b) Assume that is unknown, but we can observe X. For given 00, we want to test the
hypothesis H: 020 against the alternative H₁: 0 < 0o. Consider the test which rejects
Ho, if and only if X < c. .low should we choose c, as a function of 0o and a, to get a test
with significance level a? Carefully justify your answer.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 5 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON