STUDY GUIDE TO QUIZ 2

You are allowed ONE 8 1/2 by 11 inches set of notes (both sides)

Bring a calculator, you will be given

Binomial, Poisson, Gamma and

Normal distribution table. Also sheet with mean and variance of a number

of distributions and handwritten summary of two dimensional random variables

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## Readings:

Devore: material for hw 5 and 6 and 7,

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## Continuous Random Variables

(1) General properties for a probability density function f(x) similiar to
those above for a discrete random variable.
(2) Uniform random variable f(x; a,b) = 1(b-a) over a < x < b
(3) Normal or gaussian random variable f(x;mu, sigma)
i) how to go from X to Z by subtracting mean and dividing difference by
standard deviation
ii) how to compute probabilities of events using the cumulative normal
table in front of text
## One Dimensional Random Variables

For both discrete and continuous random variables (including the named
ones below) you should be able to:
(1) Compute the probability of X being in some interval, for example
X is AT LEAST 12 but AT MOST 15.5
(2) Compute the MEAN, MEDIAN, VARIANCE, and STANDARD DEVIATION
(3) Recognize the situation that gives rise to this type of distribution,
for example, binomial distribution arises from n independent indentical
trials with each have a success probability p. In contrast a negative
binomial arises when the number of successes r is fixed and the random
varaible is the number of trials (or failures before the rth success).
(4) shapes of Gamma and Beta densities
(5) Weibull, Lognormal, Beta , Gamma densities, how to compute proabilities
and meaan and variance
## Two dimensional random variables

(1) General properties for a TWO DIMENSIONALprobability density function
f(x,y) or probability mass function p(x,y)
similiar to those above for a one dimensional random variable.
a) compute probability of events
b) for discrete 2-dim pmf and continuous 2-dim density
compute marginals, E[h(x,y)], compute probability of an event
c) compute Covariance and correlation
d) determine independence of two random variables
e) compute conditional distributions