A cancer researcher wants to test a new combination of chemotherapy and radiation on skin tumors in laboratory mice. The researcher administers the treatment to each of four laboratory mice having the type of skin tumor under study. After a week of treatment, the researcher records failure or success for each mouse, depending on whether or not skin tumor cells are observed on the animal.    Problem 6-17 a asks us to write out the sample space for the problem. Let S represent the cancer disappears and F represents the cancer did not disappear. The sample space events are as follows: SSSS   SSSF      SSFF      SFFF      FFFF SSFS      SFFS      FSFF SFSS      FFSS      FFSF FSSS      SFSF      FFFS                             SFFS                             FSFS   Suppose that the treatment combination has no effect on the skin tumors. However, there is a .1 probability that the tumor will disappear spontane­ously over a week of observation. If the mice are independent of one an­other with regard to disappearance of the skin tumor, find the probability function for the sample space in this problem. Since the mice are independent calculate the probability for each of the events above. Note that each event  listed in the same column have the same probability of occurring, then what is the probability of each event listed in each of the  five columns? Answer to 4 decimal places and list in the order of the columns. Note format answer as 0.xxxx.   Column 1  Column 2  Column 3  Column 4  Column 5    Define a random variable X to be the number of mice that are free of skin tumors at the end of the week of treatment. Find the values X takes on and the probability that X takes on each of these values. Find the expected value, variance, and standard deviation of X. Step 1 for part d: Using the results from part b, the Random variable X is the number of mice who are free from cancer at the end of the week. Caluclate the following rounding to 4 decimal places and formating as 0.xxxx. P(X=0) = P(X=1) = P(X=2) = P(X=3) = P(X=4) =

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I want solution to STEP 1 PART D: Kindly help to explain all steps. I want to approach used to solve. Thanks a lot!

 

A cancer researcher wants to test a new combination of chemotherapy and radiation on skin tumors in laboratory mice. The researcher administers the treatment to each of four laboratory mice having the type of skin tumor under study. After a week of treatment, the researcher records failure or success for each mouse, depending on whether or not skin tumor cells are observed on the animal.   

Problem 6-17 a asks us to write out the sample space for the problem. Let S represent the cancer disappears and F represents the cancer did not disappear. The sample space events are as follows:

SSSS   SSSF      SSFF      SFFF      FFFF

SSFS      SFFS      FSFF

SFSS      FFSS      FFSF

FSSS      SFSF      FFFS

                            SFFS

                            FSFS

 

Suppose that the treatment combination has no effect on the skin tumors. However, there is a .1 probability that the tumor will disappear spontane­ously over a week of observation. If the mice are independent of one an­other with regard to disappearance of the skin tumor, find the probability function for the sample space in this problem.

Since the mice are independent calculate the probability for each of the events above. Note that each event  listed in the same column have the same probability of occurring, then what is the probability of each event listed in each of the  five columns? Answer to 4 decimal places and list in the order of the columns. Note format answer as 0.xxxx.

 

Column 1 

Column 2 

Column 3 

Column 4 

Column 5 

 

Define a random variable X to be the number of mice that are free of skin tumors at the end of the week of treatment. Find the values X takes on and the probability that X takes on each of these values. Find the expected value, variance, and standard deviation of X.

Step 1 for part d: Using the results from part b, the Random variable X is the number of mice who are free from cancer at the end of the week. Caluclate the following rounding to 4 decimal places and formating as 0.xxxx.

P(X=0) =

P(X=1) =

P(X=2) =

P(X=3) =

P(X=4) =

 

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