What is E(X|sinX) and the Distribution of E(X-Y|2X-Y)?

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In summary, the concept of "expectation" in scientific research refers to the predicted outcome of an experiment or study based on existing knowledge and theories. It plays an important role in the scientific method by guiding the research process and hypothesis development. However, common challenges such as confirmation bias and unexpected results can arise when dealing with expectations in scientific research. Scientists handle conflicting expectations by conducting further research and collaborating with others in the field. "Expectation" can also impact the validity and reliability of scientific findings if it introduces bias. Therefore, it is important for scientists to be aware of their own expectations and strive to minimize their influence on the research process.
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tennishaha
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1. If X is uniform distributed in (0,pi), what is E(X|sinX)?

2. Suppose X and Y are Gaussian random variables N(0,sigma_x) and N(0,sigma_y).
what is the distribution of E(X-Y|2X-Y)


Can anyone help?

thanks
 
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Your notation is not standard - could you clarify exactly what you mean.
 

FAQ: What is E(X|sinX) and the Distribution of E(X-Y|2X-Y)?

What is the concept of "expectation" in scientific research?

The concept of "expectation" in scientific research refers to the predicted outcome of an experiment or study based on existing knowledge and theories. It is the anticipated result that researchers hope to find through their investigations.

What is the significance of "expectation" in the scientific method?

"Expectation" plays an important role in the scientific method as it helps guide the research process and hypothesis development. By having a clear expectation of what the results should be, scientists can design experiments and analyze data in a way that supports or refutes their initial predictions.

What are common challenges that arise when dealing with "expectation" in scientific research?

One common challenge is confirmation bias, where researchers may unintentionally interpret data in a way that supports their expected outcome. Other challenges include unexpected results, which may require researchers to revise their initial expectations, and ethical concerns, where expectations may influence how data is collected or interpreted.

How do scientists handle conflicting "expectations" in their research?

When conflicting expectations arise, scientists may conduct further research to gather more evidence and data. They may also collaborate with other experts in the field or reevaluate their initial hypotheses to account for the discrepancies. In some cases, conflicting expectations can lead to new discoveries and advancements in scientific understanding.

How can "expectation" impact the validity and reliability of scientific findings?

"Expectation" can have a significant impact on the validity and reliability of scientific findings. If researchers have strong expectations that may influence their methods or interpretation of data, it can introduce bias and compromise the objectivity of the study. Therefore, it is important for scientists to be aware of their own expectations and strive to minimize their influence on the research process.

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