Math 300 , Spring 2002, Day31, M, April 15 Hit reload to get most current version

Expected values and variance:  (back to ch. 7)
Instead of sums, we have integral signs.
E(X) is still the balance point on the f(x) graph.
"Law of the unconscious statistician"--
If Y = g(X), then E(Y) = integral over all y's of y times density of Y, OR
                                = integral over all x's of g(x) times density of X.
   So E(X2) is the integral of x2 times f(x) dx.
Var(X) =  E(X2) -µ2 still.  (proof)

Algebra of expectation rules still hold:  E(cX)=cE(X),
E(Y + W) = E(Y) + E(W)  (If Y and W are both functions of some common X, you can see this simply because integration distributes over sums.  If not, we'll have to wait for chapter 5)

Find E(X) for exponential (p. 214).  Requires integration by parts (or Ash's handy formula p. 95).
Find var(X) for exponential (p.226, and p. 95)
Find E(X) for Normal (0, 1).  Find Var(X) for normal (0,1) (We'll use the fact that area under f(x) = 1)

HW:
Expected value and variance, back to Ch. 7 pp. 213=125, 225-232.  Useful integrals p. 95
Find E(X) and Var(X) for the Density sheet formula (f (x) = x - 1/2, 1<x<2).
Ash p. 221,
#1,
#2  Do the calculus, get the obvious answer.
#1, #3 (use p. 95)
#15
On handout of f and F problems (from Strait), Find E(X), E(X2), var(X) for #1 and #4
Ash p. 233
#2

next we'll return to Ch. 4, Sec.4.4, 4.5 optional, 4.6.

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