Could anyone explain to me that why:let u=E[X]. then

[rukawakaede]

could anyone explain to me that why:

let u=E[X]. then E=E[X]?

I am a bit confused. Thanks.

 

[saim_]

'u' is defined to be E[X]. It always going to be E[X]. Thus its expectation value is E[X].

 

[micromass]

In general, if X=a a.e., then E[X]=a. If you want me to prove this, then you first need to tell me how you defined expectation, since the definition tends to vary...

 

[mathman]

could anyone explain to me that why:

let u=E[X]. then E=E[X]?

I am a bit confused. Thanks.

If a random variable is constant, then its average is that constant.

 

[blue_raver22]

Of course, I would be happy to explain this to you. Let's start by defining the terms in this equation. The variable u represents the expected value of a random variable X. This means that u is the average value that we would expect to see if we were to repeat an experiment involving X many times. The notation E[X] represents the expected value of the random variable X.

Now, to answer your question, the reason why E is equal to E[X] is because the expected value operator is a linear operator. This means that it follows the properties of linearity, such as the distributive property and the property of addition. In this case, since u is a constant (the expected value of X), we can treat it as a number and use the property of addition to show that E is equal to E[X].

In simpler terms, the expected value of a constant is always equal to the constant itself. So, in this case, E is equal to u, which is equal to E[X]. I hope this explanation helps to clarify any confusion you may have had. Please let me know if you have any further questions.