Practice with Probability Density Functions
1. A 6 cc solution contains exactly one bacterium. This solution is slowly pipetted into a flask.
Let X be the RV that measures the amount of solution in the flask at the exact moment the
bacterium enters the fl
Mathematics 116 Life Sciences Calculus 2 Spring 2010
NOTES ON INFERENTIAL STATISTICS
1. The Central Limit Theorem and Sampling Distributions
1.1. Denitions and Examples. We start with the denitions and observations that link the
familiar idea of sampling
Mathematics 116 Life Sciences Calculus 2 Spring 2009
PRACTICE ON RANDOM VARIABLES
(1) Let S = cfw_(r, g ) | r, g = 1, 2, . . . , 6 be the usual sample space obtained from throwing two dice,
a red one and a green one. Dene Z by Z(r, g ) = 2r + g . So, Z ju
Mathematics 116 Life Sciences Calculus 2 Spring 2009
NOTES ON RANDOM VARIABLES
1. Introduction
1.1. Denitions and Examples. Here is the denition of a random variable [which we will sometimes just call an RV].
Denition: Let S be a probability space with pr
Math 116 - Spring 2009: Practice with Independence
Determine which of the following pairs of events are independent and which
are dependent.
For (1)-(3), my experiment is to ip a coin 10 times and record the outcome
each time. [Note: The size of the sampl
introduction
A point estimate, because it is a single number, by itself provides no infor-
mation about the precision and reliability of estimation. Consider, for ex-
ample, using the statistic )? to calculate a point estimate for the true average
breaki
410
Chapter 9: Higher Order and Systems of Differential
13.
&1
20.
+ 121' + 9
(21' + 3)2
41'2
o
o
3
-2
l'
l'
4
y
C1 + C2x
repeated
+ C2xe-3x/2
C1e-3x/2
Y
l'
o
o
o repeated
14.
twice
+ C3X2 + C4e4z
21.
1'3 +
+ 16
1'(1' + 4)2
l'
o
o
o
l'
-4 repeated
Y
C1 +
Mathematics 116 Life Sciences Calculus 2 Spring 2009
PRACTICE ON THE BINOMIAL DISTRIBUTION
(1) Suppose that a [not too smart] gambler bets on black for 100 spins of a fair roulette wheel.
The wheel has 18 black numbers, 18 red numbers and 2 green numbers