Mathematical Expectation

7 important questions on Mathematical Expectation

If a and b aare constants then: E(aX+b) =

aE(X)+b

What is the rth moment about the mean

E[(X-u)^r]

What is the standard variation?

Sqrt(var(X))
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If X and Y  are independent then

E(XY)=E(X)*E(Y) and cov(XY) = 0

State Chebyshev's Theorem

P((x-u)<ko)>=1-1/k^2 (exact)
1-1/k^2 (at least)

  1. Calculate the mean
  2. Calculate the variance
  3. Calculate the SD
  4. Integrqate from -kSD<u<kSD 

Q=4x+5Y+6Z, give var(Q), also give COV(Q,C), C=6X+2Y+Z

.

How to calculate the conditional density of x given y=y

  1. f(x|y)=... (fill in given y)
  2. E(X|y)=int(xf(x|y))
  3. E(X^2|y)=inf(x^2(f(|y)))
  4. var = 3-2^2

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