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 F_x(x) into its inverse using the formula: F^-1_x(x) = 1/F_x(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.
_______

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 F_x(x) into its inverse using the formula: F^-1_x(x) = 1/F_x(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.

orchestra answered 2 years ago

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