Question

In: Statistics and Probability

Indicate whether each of the following statements is true or false. a. The Χ2 test is...

Indicate whether each of the following statements is true or false.
a. The Χ2 test is used to compare the goodness of fit between a set of measurements and a theoretical distribution.
_______
b. The variance of a random variable is always greater than or equal to zero.
_______
c. The maximum likelihood estimate for some parameter represents the value that should happen
most frequently. For example, the maximum likelihood estimate for the outcome of rolling a pair
of 6-sided dice is "7".
_______
d. If we generate a 99% confidence interval for the mean of some value using 100 independent replications of a simulation model, then the interval will usually be too small to contain 20 out of the
100 samples.
_______
e. One step in generating random variables with other distributions is to convert the cumulative distribution function Fx(x) into its inverse using the formula: F-1x(x) = 1/Fx(x).
_______
f. For a discrete random variable, the cumulative distribution function looks like a series of disconnected horizontal "steps" going upwards.
_______
g. If you are not using the data to estimate the sample variance, then you can should calculate your
confidence intervals using the normal distribution instead of the Student’s t-distribution, even
when the number of samples is small.
_______
h. In a time-driven program structure, the simulation clock advances by a fixed amount at each iteration, but the number of events executed varies from one iteration to another.
_______
i. If the event list is implemented as a heap, then the time to insert a new event into the list is O(n)
and the time to remove the next event is also O(n).
_______
j. Common random numbers is a variance reduction technique for simulation programs in which
you must use a single stream of random numbers for every random variable in your program.
_______

Solutions

Expert Solution

a. The Χ2 test is used to compare the goodness of fit between a set of measurements and a theoretical distribution.
_TRUE______


b. The variance of a random variable is always greater than or equal to zero.
__TRUE_____


c. The maximum likelihood estimate for some parameter represents the value that should happen
most frequently. For example, the maximum likelihood estimate for the outcome of rolling a pair
of 6-sided dice is "7".
__FALSE_____


d. If we generate a 99% confidence interval for the mean of some value using 100 independent replications of a simulation model, then the interval will usually be too small to contain 20 out of the
100 samples.
___TRUE____


e. One step in generating random variables with other distributions is to convert the cumulative distribution function Fx(x) into its inverse using the formula: F-1x(x) = 1/Fx(x).
__TRUE_____


f. For a discrete random variable, the cumulative distribution function looks like a series of disconnected horizontal "steps" going upwards.
__TRUE_____


g. If you are not using the data to estimate the sample variance, then you can calculate your
confidence intervals using the normal distribution instead of the Student’s t-distribution, even
when the number of samples is small.
___FALSE____



j. Common random numbers is a variance reduction technique for simulation programs in which
you must use a single stream of random numbers for every random variable in your program.
___TRUE____

h. In a time-driven program structure, the simulation clock advances by a fixed amount at each iteration, but the number of events executed varies from one iteration to another.
_______


i. If the event list is implemented as a heap, then the time to insert a new event into the list is O(n)
and the time to remove the next event is also O(n).
_______

These two questions are from computer science, so please tag them in computer science.


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