Construct F2,3, i.e., a F distributed random variable with (2, 3) degrees of freedom Construct I(2.5, 12), i.e., a Gamma distribution with shape = 2.5 and scale 12.
Construct F2,3, i.e., a F distributed random variable with (2, 3) degrees of freedom Construct I(2.5, 12), i.e., a Gamma distribution with shape = 2.5 and scale 12.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.4: Discrete Random Variables; Applications To Decision Making
Problem 14E
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![[Hint_1]
In class, we saw that if we are given two random variables X~X and Y X the distribution
of (X/n)/(Y/m) is given by
Also, in the midterm we saw that
X/n
Y/m
F₁,m
T (k, 2) = x₂k1
i.e., A Gamma distribution with parameters (k, 2) is a Chi-squared distribution with 2k degrees of
freedom. Similarly, if c> 0 is some constant then
cX~I(α₁, cp),
i.e., multiplying a Gamma distribution by c results in a new Gamma distribution with the same
shape a₁ but the scale becomes cß.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd7c2748e-5ba1-4f2f-bc7d-c6e1ab8bba12%2Fc8bff742-6841-45f6-99dd-7f55a81249f0%2Fbw52jmh_processed.png&w=3840&q=75)
Transcribed Image Text:[Hint_1]
In class, we saw that if we are given two random variables X~X and Y X the distribution
of (X/n)/(Y/m) is given by
Also, in the midterm we saw that
X/n
Y/m
F₁,m
T (k, 2) = x₂k1
i.e., A Gamma distribution with parameters (k, 2) is a Chi-squared distribution with 2k degrees of
freedom. Similarly, if c> 0 is some constant then
cX~I(α₁, cp),
i.e., multiplying a Gamma distribution by c results in a new Gamma distribution with the same
shape a₁ but the scale becomes cß.
![Let
Using Z1, Z2,..., Z5 and [Hint_1]:
1.
Z1, Z2,..., Z5 N(0, 1).
tid
Construct F2,3, i.e., a F distributed random variable with (2, 3) degrees of freedom
2.
Construct I'(2.5, 12), i.e., a Gamma distribution with shape = 2.5 and scale = 12.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd7c2748e-5ba1-4f2f-bc7d-c6e1ab8bba12%2Fc8bff742-6841-45f6-99dd-7f55a81249f0%2F6i9xiej_processed.png&w=3840&q=75)
Transcribed Image Text:Let
Using Z1, Z2,..., Z5 and [Hint_1]:
1.
Z1, Z2,..., Z5 N(0, 1).
tid
Construct F2,3, i.e., a F distributed random variable with (2, 3) degrees of freedom
2.
Construct I'(2.5, 12), i.e., a Gamma distribution with shape = 2.5 and scale = 12.
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