Explain random sampling and why it is important.
Give examples of independent and dependent events.
Solution
Random sample is a procedure for sampling from a population in which
(a) the selection of a sample unit is based on chance and
(b) every element of the population has a known, non-zero probability of being selected.
Random sampling helps produce representative samples by eliminating voluntary response bias
and guarding against undercoverage bias. All good sampling methods rely on random sampling.
The myth: \"A random sample will be representative of the population\".
In fact, this statement is false -- a random sample might, by chance, turn out to be anything but
representative. For example, it is possible (though unlikely) that if you toss a fair die ten times,
all the tosses will come up six. If you find a book or web page that gives this reason, apply some
healthy skepticism to other things it claims.
The real reason: The mathematical theorems which justify most frequentist statistical procedures
apply only to random samples.
INDEPENDENT EVENT
A drawer contains 3 red paperclips, 4 green paperclips, and 5 blue paperclips. One paperclip is
taken from the drawer and then replaced. Another paperclip is taken from the drawer. What is the
probability that the first paperclip is red and the second paperclip is blue?
Because the first paper clip is replaced, the sample space of 12 paperclips does not change from
the first event to the second event. The events are independent.
P(red then blue) = P(red).
Explain some potential downsides of Digital Predistortion (DPD) appl.pdf
1. Explain some potential downsides of Digital Predistortion (DPD) application in modern and
emerging radar systems.
Solution
- - No implication of DPD are capable of making use of the linear shift invariant (LSI) system
properties as by definition they are nonlinear and not shift-invariant although they are often
approximated as shift-invariant (memoryless).
-- Very High-speed channel is required b/w different channel sources in order to adapt the digital
pre-distorter & apply the pre-distortion as each source must have the channel information from
each and every one of the other sources as will be shown in the derivation and approaches
sections.
