Suppose that I am interested in the number of mutations at ONE d location for 100 patients. X-"#patients with mutation" be the random variable. The size of this dom variable is 100
Suppose that I am interested in the number of mutations at ONE d location for 100 patients. X-"#patients with mutation" be the random variable. The size of this dom variable is 100
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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![1 a. Suppose that I am interested in the number of mutations at ONE
fixed location for 100 patients.
Let X- #patients with mutation" be the random variable. The size of this
random variable is 100
1 b. Suppose that I know somehow that the probability of mutation at
that position is 0.001. The probability of success of X is
1c Suppose that I OBSERVE that 1 out of 100 patients showed
mutation. So, X-1 happened. Based on this one observation, use a
formula taught in class to get the MLE of probability of success. The mle
of pis
|. (Write it as a decimal, not a fraction)
1d. Next, suppose that I am interested in the number of mutations at 10
locations for 100 patients. I somehow know that the probability of
mutation is the same at all the 10 locations. I have the following
observation vector.
X-(0,0.0.00.0,00.0,1)
Here XI 1] is the number of patients with mutation at Position 1, X[ 2| is
the same for Position 2, and so on. Using this observation vector, find an
MLE of p. The MLE of p using the new observation vector is
le. The position number which showed one patient out of 100 had a
. (Hint: It is a number between 1 and 10,
mutation is
assuming the positions are numbered 1 through 10.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7eb30b7e-9eb6-4219-970e-d5fc12b9e88b%2F0e990c59-385e-4277-93e3-21ad9bd93862%2Fpu0z9gf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1 a. Suppose that I am interested in the number of mutations at ONE
fixed location for 100 patients.
Let X- #patients with mutation" be the random variable. The size of this
random variable is 100
1 b. Suppose that I know somehow that the probability of mutation at
that position is 0.001. The probability of success of X is
1c Suppose that I OBSERVE that 1 out of 100 patients showed
mutation. So, X-1 happened. Based on this one observation, use a
formula taught in class to get the MLE of probability of success. The mle
of pis
|. (Write it as a decimal, not a fraction)
1d. Next, suppose that I am interested in the number of mutations at 10
locations for 100 patients. I somehow know that the probability of
mutation is the same at all the 10 locations. I have the following
observation vector.
X-(0,0.0.00.0,00.0,1)
Here XI 1] is the number of patients with mutation at Position 1, X[ 2| is
the same for Position 2, and so on. Using this observation vector, find an
MLE of p. The MLE of p using the new observation vector is
le. The position number which showed one patient out of 100 had a
. (Hint: It is a number between 1 and 10,
mutation is
assuming the positions are numbered 1 through 10.)
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