Proving Summation nCk p^k q^n-k =1

Thread starter sajee3a
Start date Sep 13, 2010

In summary, to prove a hypothesis, one must collect and analyze data using scientific methods and statistical analysis. Conducting a controlled experiment is important for isolating variables and ensuring reliable results. Validity of results can be ensured by using appropriate methods and replicating the experiment. Peer review plays a crucial role in evaluating the quality and accuracy of scientific claims. To effectively communicate findings, one should use clear language, provide supporting evidence, and acknowledge limitations or potential sources of error in the study.

Sep 13, 2010

sajee3a

1)given that: (1+x)^n=summation nCk X^K

PROVE: SUMMATION nCk p^k q^n-k =1, where p+q=1
2) prove the general law of addition: P(E1 U E2 U...U En)=sum P(Ei)-sum P(EiEj)+sum P(EiEjEk)-...(-1)^n-1 P(E1E2...En)

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Sep 13, 2010

mathman

Science Advisor

For 1:
1=(p+q)ⁿ=qⁿ(1+(p/q))ⁿ=qⁿΣnCk(p/q)^k=ΣnCkp^kq^n-k

FAQ: Proving Summation nCk p^k q^n-k =1

How do I prove a hypothesis?

To prove a hypothesis, you must collect and analyze data that supports or refutes your hypothesis. This may involve conducting experiments, making observations, or using other scientific methods to gather evidence. Once you have collected enough evidence, you can use statistical analysis to determine if your results are significant and support your hypothesis.

What is the importance of conducting a controlled experiment?

A controlled experiment allows for the isolation of a particular variable and its effect on the outcome of the experiment. This helps to ensure that any observed changes are a result of the variable being tested, rather than other factors. It also allows for the comparison of results between different groups, providing more reliable evidence to support a hypothesis.

How can I ensure the validity of my results?

To ensure the validity of your results, you should use appropriate and reliable methods to collect and analyze data. This may include using standardized procedures, using a large sample size, and controlling for any potential confounding variables. It is also important to replicate the experiment to ensure consistent results.

What is the role of peer review in proving scientific claims?

Peer review is a process where experts in the same field review and critique the research and findings of a study before it is published. This helps to ensure the quality and accuracy of scientific claims by identifying any errors or biases in the research. It also allows for the evaluation of the methodology and results by other scientists in the field.

How can I communicate my findings effectively?

To communicate your findings effectively, you should use clear and concise language and provide supporting evidence for your claims. This may include using graphs, charts, and tables to visually represent your data. It is also important to provide a thorough explanation of your methods and results, and to acknowledge any limitations or potential sources of error in your study.