Chapter 5 MIS 301
x is a random variable with the prob. function f(x) = x/6 for x = 1,2 or 3. the expected value of x is
2.333
1 hour, how many cars arrived
DRV
20 question test- answered correctly
DRV
audit 50 tax returns- how many have errors
DRV
the weight of an object measured in grams is an example of
a continuous random variable
the binomial prob. distribution is used with
a discrete random variable
variance is
a measure of the dispersion of a a random variable
random variable
a random variable is a numerical description of the outcome of an experiment
continuous random variable
a random variable that may assume any numerical value in an interval or collection of intervals
discrete random variable
a random variable that may be finite # of values or an infinite sequence of values such as any #
a continuous random variable may assume
any value in an interval or collection of intervals
an experiment consists of measuring the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is speed, measured in miles per hour. this is a
continuous random variable
Discrete prob. Distribution
defines the prob. distribution for a discrete random variable. has to be bigger than 0. and the sum of prob. has to =1 1/n = f(x)
exhibit 5-11, the prob. that there are less than 3 occurrences
idk how but it i .1016
Exhibit 5-11 The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. Refer to Exhibit 5-11. The expected value of the random variable x is
just the mean, 5.3
expected value for binomial dis.
np
variance for binomial dis.
np (1-p)
Exhibit 5-11 The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. Refer to Exhibit 5-11. The random variable x satisfies which of the following probability distributions?
poission
poisson
the prob. of an occurrance is the same for any two intervals, common intervals are measured in time distance area and volume. The occurrance or nonoccurrance in any interval is independent of the occurrence or nonoccurrence in any other interval
what is not a char. of an experiment where the binomial prob. distribution is applicable
the trials are dependent
which is a characteristic of binomial experiment
trials are independent
hypergeometric prob. distribution
used to compute the prob. that in a random selection of n elements selected without replacement we obtain x elements labeled success and n-x elements labeled failure trials are not independent the prob. of success changes from trial to trial r= number of elements
4% of the customers of a mortgage company default on their payments. a sample of 5 is selected, whats the prob. of 2 defaulting
.0142
in a binomial experiment the prob. of success is .06. What is the prob. of two successes in seven trials
.0555
exhibit 5-2. The prob. distribution for the daily sales are given, what are the expected daily sales
56,000
the variance for the binomial prob. distribution is
Var(x)=np(1-p)
exhibit 5-11 the prob. that there are 8 occurrences in 10 minutes is
.0771
assume that you have binomial experiment with p=.5 and sample size of 100 the expected value of distribution is
50
5-4, the prob. of sales at least of 50000
90%
observe an employees work- # of unproductive hours in an 8 hour work day
CRV
weight of shipment- # of pounds
CRV
the poisson prob. distribution is a
discrete prob. distribution
a random variable that can assume only a finite # of values is
discrete random variable
an experiment consists of making 80 calls in order to sell a particular insurance policy. The random variable in this experiment is the # of sales made. This random variable is a
discrete random variable
the # of customers that enter a store during one day is an example of
discrete random variable
expected value of a binomial prog. distribution is
e(x)=np
a measure of the average value of a random variable is called
expected value
a weighted average of the value of a random variable where the prob. function provides weights is known as
expected value
in the textile industry a manufacturer is interested in the # of blemishes occurring in each 100 feet. the prob. distribution that has the greatest chance of applying to this situation is
poisson distribution
the key difference between the binomial and hypergeometric distribution is that with the hypergeometric distribution the
prob. of success changes from trial to trial
in a binomial experiment the
prob. of success does not change from trial to trial
binomial prob distribution
sequence of n identical trials, two outcomes, chance of success does not change, trials are independent
variance for DRV
sum ( x- u)^2 (f(X)
expected value of a discrete random variable
sum(x x (fx))
