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Midterm

# MAS 311 Test 2.pdf

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University of Miami

Management Science

MAS 311

Donno

Spring

Description

Discrete Uniform Probability Distribution Multivariate Hypergeometric Probability Distribution
The Values of the random variable are equally likely If N items can be partitioned into the k cells A1,A2,....Ak with
a1,a2,....,ak elements, respectively, then the probability
distribution of the random variables X1,X2,....,Xk, representing
the number of elements selected from A1,A2,....,Ak in a random
sample of size n, is
K= number of values random variable may assume
Binomial Probability Distribution
1. Sequence of n identical trials
2. Two outcomes (success & failure) are possible in each trial
3. Probability of success (p) does not change in each trial Negative Binomial Probability Distribution
4. Trials are independent 1. Consists of a sequence of n identical trials
2. Two outcome (success & failure) are possible in each trial
3. Probability of success (p) doesn’t change from trial to trial
4. Trial are independent
5. Trials will be repeated until a ﬁxed number of successes occur
(probability that the kth success occurs on the xth trial)
X = Number of successes
P = Probability of success in one trial
n = Number of trials
f(x) = Probability of x successes in n trials
p = probability of success
Multinomial Probability Distribution q = probability of failure
1. Consists of n repeated trials
2. Each trial has a discrete number of possible outcomes Geometric Probability Distribution
3. The probability that a particular outcome will occur is If repeated, independent trials can result in a success with
constant in each trial probability p and a failure with probability
4. The trials are independent (outcome of one trial doesn’t affect q = 1 - p, then the probability distribution of random variable X,
outcome of others) the number of the trial on which the 1st success occurs is:
Poisson Probability Distribution
Hypergeometric Probability Distribution - Used to estimate the number of occurrences over a speciﬁed
1. Sequence of n identical trials interval of time or space
2. Two outcomes (success & failure) are possible in each trial - A Poisson distributed random variable is a discrete random
3. Probability of success does change from trial to trial variable that may assume an inﬁnite sequence of values ( x =
4. Trials are not independent 0,1,2, ... )
1. The probability of an occurrence must be the same for any

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