How to calculate MEAN of exponential distribution?

8,619

Hints: for $E[X+5]$ use the linearity of expectation. What is $E[5]$?

For $E[(X+5)^2]$ you can go back to the definition $$E[(X+5)^2]=\displaystyle \int_0^{\infty} \dfrac{(x+5)^2\exp(\frac{-x}{5})\; dx}{5}$$ or you can expand out $E[(X+5)^2]=E[X^2]+2E[X]E[5]+E[5^2]$

Share:
8,619

Related videos on Youtube

Rick
Author by

Rick

Updated on June 16, 2022

Comments

  • Rick
    Rick about 2 hours

    $ f(x) = \begin{cases} \frac15 e^{(-\frac15x)}, x>0 \\ 0, \text{elsewhere}\\ \end{cases}$

    How to calculate $E[(X+5)]$ and $E[(X+5)^2]$ ?

    Thanks a lot.

    • Nikita Evseev
      Nikita Evseev over 9 years
      Do you know what $E[X]$ is?
    • Inquest
      Inquest over 9 years
      $$\displaystyle \int_0^{\infty} \dfrac{(x+5)\exp(\frac{-x}{5})}{5}$$
    • Did
      Did over 9 years
      What did you try and what is STOPPING you?
    • Rick
      Rick over 9 years
      I know $E[X]$ means the mean/expected value of $f(x)$
    • Rick
      Rick over 9 years
      I know $E[X]$ = 5 but I've no idea about $E[(X+5)^2]$
  • Rick
    Rick over 9 years
    Is $E[X] = \frac1\lambda $? Then $E[X] = 5$. Can we use the similar method to find out $E[(x+5)^2]$ ?
  • Ross Millikan
    Ross Millikan over 9 years
    Yes, $E[X]=5$ The way you find that (if you don't look it up) is the integral Inquest gave without the +5. The integral in my answer is the same method for $E[(X+5)^2]$ Can you do it?
  • Rick
    Rick over 9 years
    Can you explain a little bit more on $E((X+5)2)=E(X2)+10E(X)+5$? I'm quite confused.
  • Rick
    Rick over 9 years
    Sorry. Can you show the steps why $E[(X+5)^2]=E[X^2]+2E[X]+E[5^2]$?
  • Rick
    Rick over 9 years
    Why it's not $E[(X+5)^2]=E[X^2]+10E[X]+E[5^2]$ but $+2E[X]$?
  • Rick
    Rick over 9 years
    Why it's not $E[(X+5)^2]=E[X^2]+10E[X]+E[5^2]$ but $+5$?
  • Ross Millikan
    Ross Millikan over 9 years
    @Rick: You are right, I dropped the $E[5]$. Fixed.
  • Michael Hardy
    Michael Hardy over 9 years
    Sorry --- typo: It's $5^2$.