1. (a) For each of x = 1, 2, 3, 4, 5, 6 find a ∈...
1. (a) For each of x = 1, 2, 3, 4, 5, 6 find a ∈ {0, 1, ..., 6}
where x 2 ≡ a (mod 7).
(b) Does x 2 ≡ a (mod 7) have a solution for x every integer a?
Justify your answer!
(c) For a ∈ {1, ..., 6} (so a not equal to 0!), how many
solutions for x are there in the equation x 2 ≡ a (mod 7)?
What is the pattern here?
In some implementations of “regular expressions,” the notations
\1, \2, and so on can occur in...
In some implementations of “regular expressions,” the notations
\1, \2, and so on can occur in a search pattern. For example,
consider the search pattern ^([a-zA-Z]).*\1$. Here, \1 represents a
recurrence of the same substring that matched [a-zA-Z], the part of
the pattern between the first pair of parentheses. The entire
pattern, therefore, will match a line of text that begins and ends
with the same letter. Using this notation, write a pattern that
matches all strings in the language...
Here is some empirical data: { 1, 2, 1, 4, 5, 3, 1, 2, 2, 1,...
Here is some empirical data: { 1, 2, 1, 4, 5, 3, 1, 2, 2, 1, 1,
3, 5, 1, 3, 2, 1, 2, 5, 2, 4, }. Create a Python program that draws
a random number from the empirical distribution of this data
Suppose you went to a fundraiser and you saw an interesting
game. The game requires a...
Suppose you went to a fundraiser and you saw an interesting
game. The game requires a player to select five balls from an urn
that contains 1000 red balls and 4000 green balls. It costs $20 to
play and the payout is as follows:
Number of red balls
Prize
0
$0
1
$20
2
$25
3
$50
4
$100
5
$200
Questions:
1) Is this a binomial experiment? If so, explain what p, q, n,
and x represent and find...