a) because it is equal to the area of the shaded region between X=4 and X=6, and the probability that X falls within some interval is given by the area under the PDF.
b) because the shaded region is a rectangle of height 1/5 (by virtue of X following a uniform distribution over the interval [2, 7], which has length 5).
Answer:
c.negative
True, by definition since the variance take in count the differences around the mean squared, then we can't have a negative value for a sum of square values.
Step-by-step explanation:
We need to remember that the variance is a measure of dispersion for a dataset respect to a measure of central tendency called the mean. The mean is defined as:
And the population mean is given by:
The population variance is defined by:
And the sample variance is defined as:
Now if we analyze the options we have this:
a.zero
False, if all the values are the same then the mean would be the same to the values and the difference between each value and the mean would 0 and indeed the variance would be 0.
b.larger than the standard deviation
False, if the population standard deviation is then the variance would be
and as we can see is higher than the standard deviation
c.negative
True, by definition since the variance take in count the differences around the mean squared, then we can't have a negative value for a sum of square values.
d.smaller than the standard deviation
False, if the population standard deviation is then the variance would be
and as we can see is lower than the standard deviation