Midterm due today. Geometric?
No class Friday. Go be Active! Email me if you want to meet for questions etc.
Quiz Next class (Mon.): Closed book, Expected
value stuff, chosen from:
(for
sure) Deriving,
E(X(X-1))of Poisson.
(one
from) Var(X) from E(X(X-1))
and E(X) (how to find & why)
Proofs for Var and Cov alternate formulas. Var(X+Y) = Var(X) +
Var(Y)
+2Cov(X,Y) (derivation )
(one from) True/false: X,Y Independent <=?=>
E(XY)=0, Cov(X,Y)=0 (like Ash HW p.223 # 14)
HW: Read 4.1.
Note: f(x) = |x| is "already" a piecewise function:
f(x) = x if x > 0, = -x if x < 0 See p. 96
for examples
of use.
p. 103-4, #1 thru 6
Read ahead pp.104 to 114. (You can do the following problem
whether
or not the reading makes sense.)
Some more continuous probability problems:
Handout
"Density problems"
Do #1, 3b, 4b, 5 Hand in!
Read 4.2 pp.104 to 114. Discrete to start with. Then
continuous, then mixed.
Discrete CDF's:
A. Poisson Distribution: Use the Poisson table handout Poisson
table to find, for lambda = 2.2,
P(X< 4), P(X > 4), P(X =
2), P(2 < X < 4), P(2 < X < 4)
B. Use M&M's binomial table (Table
C) (or the Excel version), and construct
a table column for B(4, .5) which tables F(x). Check with the Cumulative binomial table here.
(Many books give cumulative tables.) Also Graph it.
Find P(1 < X < 4) from M&M's table, and from the
cumulative table. Show your work.
Ash p. 118, #1 Write the formula for F(x) carefully, paying
attention
to endpoints.(do graph both graphs)
HW:
Continuous CDF: graphing
A. Normal Distribution: Tables often
give cumulative distributions; almost always for Normal. (There is a table
on p. 129, Ash--"Unit normal", or use the one in M&M, or here).
B. Density-->CDF
handout: Graph
CDF by counting squares, carefully. Calculate formula next
time(s).
C. 151 Densities to CDF
Graph
CDFs --counting squares is already done. Calculate formulas next
time(s).
Ch. 4, Continuous distributions--outcome is a measure, not a count. Spinner!
Density curve: f(x) >
0, with total area under f(x) = 1 "Probability density function"
= "pdf"
Probability = Area under the curve.
P(a<X<b) = area between a and b. continued.
Details Day 22
4.2: Cumulative Distribution Function
(CDF,
"Distribution Function")
F(x) = P(X <
x).
Defined for every x on the real line. Capital letter.
(pdf
uses small letter)
Continuous: Area to the left of x
under
the density. Continuous function.
P(a < X < b) = F(b) -
F(a)
(You used this to find Normal probabilities in Statistics)
Discrete: Sum of probabilities to the
left
of x (including x). Jumps at each lump. "Step function."
See Poisson
table ---shows the step function
P (X < a) = F(a), P (X <
b) = F(b), so
P (a < X < b) = F(b) -
F(a)
(note missing = at left end) Must watch ends carefully
Details Day 22
| Sievers home | Math300-Sp08Day23.htm | 2:30pm | 3/26/08 |