NATS 1575 Lecture Notes - Lecture 43: Hemileia Vastatrix

Science Grade 9 Chemistry:

You are doing an experiment to see if drinking coffee at breakfast improves your marks. You divide your class into 2 groups. Group A drinks coffee in the morning and Group B does not drink coffee. When the students come into class you have them write a test. You found the average mark for Group A was 75% and the average mark for Group B 90%. (6 marks)

What is the independent variable in your study?

What is the dependent variable in your study?

What is the control group in your study?

List 2 controls you should have in your study.

What is your conclusion for the study?

Science Grade 9:

Mr. Zajac wants to conduct an experiment to see if Red Bull energy drink makes plants grow faster. He takes plant #1 and puts it on a ledge that gets lots of sunshine. He waters this plant with 100 mL of water everyday. He takes plant #2, puts it on the ledge beside plant #1, and pours 100 mL of Red Bull on it twice a day, once when he wakes up, and once before he goes to bed. (3 marks)

a. Is this a fair test? Explain why or why not. (2 marks)

b. What would you recommend to Mr. Zajac to fix his experiment?

1.Write a function encipher(s, n) that takes as inputs an arbitrary string s and a non-negative integer n between 0 and 25, and that returns a new string in which the letters in s have been "rotated" by n characters forward in the alphabet, wrapping around as needed. For example:

>>> encipher('hello', 1) result: 'ifmmp'

>>> encipher('hello', 2) result: 'jgnnq'

>>> encipher('hello', 4) result: 'lipps'

Upper-case letters should be "rotated" to upper-case letters, even if you need to wrap around. For example:

>>> encipher('XYZ', 3)

result: 'ABC'

Lower-case letters should be "rotated" to lower-case letters:

>>> encipher('xyz', 3)

result: 'abc'

Non-alphabetic characters should be left unchanged:

>>> encipher('#caesar!', 2)

result: '#ecguct!'

Hints/reminders:

You can use the built-in functions ord and chr convert from single-character strings to integers and back:

>>> ord('a')

result: 97

>>> chr(97)

result: 'a'

You can use the following test to determine if a character is between 'a' and 'z' in the alphabet:

if 'a' <= c <= 'z':

A similar test will work for upper-case letters.

We recommend writing a helper function rot(c, n) that rotates a single character c forward by n spots in the alphabet. We have given you a template for this helper function in ps3pr3.py that checks to ensure that c is a single-character string. We wrote rot13(c) in lecture; rot(c, n) will be very close to rot13(c)! You can test your rot(c, n) as follows:

>>> rot('a', 1)

result: 'b'

>>> rot('y', 2)

result: 'a'

>>> rot('A', 3)

result: 'D'

>>> rot('Y', 3)

result: 'B'

>>> rot('!', 4)

result: '!'

Once you have rot(c, n), you can write a recursive encipher function.

Once you think you have everything working, here are three more examples to try:

>>> encipher('xyza', 1)

result: 'yzab'

>>> encipher('Z A', 2)

result: 'B C'

>>> encipher('Caesar cipher? I prefer Caesar salad.', 25)

result: 'Bzdrzq bhogdq? H oqdedq Bzdrzq rzkzc.'

2.Write a function decipher(s) that takes as input an arbitrary string s that has already been enciphered by having its characters "rotated" by some amount (possibly 0). decipher should return, to the best of its ability, the original English string, which will be some rotation (possibly 0) of the input string s. For example:

>>> decipher('Bzdrzq bhogdq? H oqdedq Bzdrzq rzkzc.')

result: 'Caesar cipher? I prefer Caesar salad.'

Here are two more examples:

>>> decipher('Hu lkbjhapvu pz doha ylthpuz hmaly dl mvynla lclyfaopun dl ohcl slhyulk.')

result: 'An education is what remains after we forget everything we have learned.'

>>> decipher('python')

result: 'eniwdc'

------------------------------------

def rot(c, n):
    """ your docstring goes here """
    # check to ensure that c is a single character
    assert(type(c) == str and len(c) == 1)

def letter_prob(c):
    """ if c is the space character (' ') or an alphabetic character,
        returns c's monogram probability (for English);
        returns 1.0 for any other character.
        adapted from:
       
    """
    # check to ensure that c is a single character   
    assert(type(c) == str and len(c) == 1)

    if c == ' ': return 0.1904
    if c == 'e' or c == 'E': return 0.1017
    if c == 't' or c == 'T': return 0.0737
    if c == 'a' or c == 'A': return 0.0661
    if c == 'o' or c == 'O': return 0.0610
    if c == 'i' or c == 'I': return 0.0562
    if c == 'n' or c == 'N': return 0.0557
    if c == 'h' or c == 'H': return 0.0542
    if c == 's' or c == 'S': return 0.0508
    if c == 'r' or c == 'R': return 0.0458
    if c == 'd' or c == 'D': return 0.0369
    if c == 'l' or c == 'L': return 0.0325
    if c == 'u' or c == 'U': return 0.0228
    if c == 'm' or c == 'M': return 0.0205
    if c == 'c' or c == 'C': return 0.0192
    if c == 'w' or c == 'W': return 0.0190
    if c == 'f' or c == 'F': return 0.0175
    if c == 'y' or c == 'Y': return 0.0165
    if c == 'g' or c == 'G': return 0.0161
    if c == 'p' or c == 'P': return 0.0131
    if c == 'b' or c == 'B': return 0.0115
    if c == 'v' or c == 'V': return 0.0088
    if c == 'k' or c == 'K': return 0.0066
    if c == 'x' or c == 'X': return 0.0014
    if c == 'j' or c == 'J': return 0.0008
    if c == 'q' or c == 'Q': return 0.0008
    if c == 'z' or c == 'Z': return 0.0005
    return 1.0