text: 1. random variable
  
  Let $\displaystyle \mu$ and $\displaystyle \sigma^{2}$ denote the mean and variance of the random variable X. Determine $\displaystyle E[\frac{(X-\mu)}{\sigma}]$ and $\displaystyle E{[\frac{(X-\mu)}{\sigma}]^{2}}.$Thank you for your help.
  
  2. Hello,
  Originally Posted by laser
  Let $\displaystyle \mu$ and $\displaystyle \sigma^{2}$ denote the mean and variance of the random variable X. Determine $\displaystyle E[\frac{(X-\mu)}{\sigma}]$ and $\displaystyle E{[\frac{(X-\mu)}{\sigma}]^{2}}.$Thank you for your help.
  Remember this : $\displaystyle \mathbb{E}(aX+b)=a\mathbb{E}(X)+b$
  
  For the second one, by seeing your latex code, I guess you actually meant :
  $\displaystyle \mathbb{E}\left(\left[\frac{(X-\mu)}{\sigma}\right]^2\right)$
  
  Note that, by definition of the variance, it equals $\displaystyle \text{Var}\left(\frac{(X-\mu)}{\sigma}\right)+\left(\mathbb{E}\left(\frac{( X-\mu)}{\sigma}\right)\right)^2$
  
  And remember that $\displaystyle \text{Var}(aX+b)=a^2 \text{Var}(X)$
  
  You should know have all the necessary stuff for answering your questions
explanation: The document contains a math question and a detailed explanation that serves as an answer to the question. The question asks for the expected values of two expressions involving a random variable, and the answer provides the necessary steps and formulas to solve the problem.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: 1. random variable
  
  Let $\displaystyle \mu$ and $\displaystyle \sigma^{2}$ denote the mean and variance of the random variable X. Determine $\displaystyle E[\frac{(X-\mu)}{\sigma}]$ and $\displaystyle E{[\frac{(X-\mu)}{\sigma}]^{2}}.$Thank you for your help.
  
  2. Hello,
  Originally Posted by laser
  Let $\displaystyle \mu$ and $\displaystyle \sigma^{2}$ denote the mean and variance of the random variable X. Determine $\displaystyle E[\frac{(X-\mu)}{\sigma}]$ and $\displaystyle E{[\frac{(X-\mu)}{\sigma}]^{2}}.$Thank you for your help.
  Remember this : $\displaystyle \mathbb{E}(aX+b)=a\mathbb{E}(X)+b$
  
  For the second one, by seeing your latex code, I guess you actually meant :
  $\displaystyle \mathbb{E}\left(\left[\frac{(X-\mu)}{\sigma}\right]^2\right)$
  
  Note that, by definition of the variance, it equals $\displaystyle \text{Var}\left(\frac{(X-\mu)}{\sigma}\right)+\left(\mathbb{E}\left(\frac{( X-\mu)}{\sigma}\right)\right)^2$
  
  And remember that $\displaystyle \text{Var}(aX+b)=a^2 \text{Var}(X)$
  
  You should know have all the necessary stuff for answering your questions
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and a detailed explanation that serves as an answer to the question. The question asks for the expected values of two expressions involving a random variable, and the answer provides the necessary steps and formulas to solve the problem.
  
  Label: question-and-answer