Suppose that you pick a bit string
from the set of all bit strings of length ten. Find the probability
that
the bit string has exactly two 1s;
the bit string begins and ends with 0;
the bit string has the sum of its digits equal to seven;
the bit string has more 0s than 1s;
the bit string has exactly two 1s, given that the string begins
with a 1.
Suppose that you pick a bit string from the set of all bit
strings of length ten. Find the probability that
the bit string has exactly two 1s;
the bit string begins and ends with 0;
the bit string has the sum of its digits equal to seven;
the bit string has more 0s than 1s;
the bit string has exactly two 1s, given that the string begins
with a 1.
How many bit strings of length 8 if i. bit strings start with
the bit 1; ii. bit strings end with the two bits 00; iii. bit
strings either start with the bit 1 or end with the bits 00.؟
Show all calculation details by not using a calculator or Excel
answers. Consider the data set: (7,11), (10,0), (13,-2).
A. Compute and interpret the coefficient of correlation.
B. Compute the least squares line for this data (no need to
repeat computations from above).
Q6. Perform the following operations using bit masking.
(a)
Set the bit 3 of a byte data
(b)
Clear the bit 5 of a byte data
(c)
Toggle the bit 7 of a byte data
(d)
Check the bit 0 of a byte data
1. How many 12-bit strings (that is, bit strings of length 14)
start with the sub-string 011?
2. You break your piggy bank to discover lots of pennies and
nickels.
You start arranging them in rows of 6 coins.
How many coins would you need to make all possible rows of 6
coins (not necessarily with equal numbers
of pennies and nickels)?
3. How many shortest lattice paths start at (4, 4) and end at
(13, 13)?
4. What is...
1. Provide a regular expression that describes all bit-strings
that length is at least one and at most three.
2. Provide a regular expression that describes all bit strings
with odd length.
Sample statistics: For the following data set, show all
details of your calculations: {9, 6, -1, 2, 0, 5,
8,3}.
a) the median
b) the standard deviation
c) Q3. Give an explanation of the method you used to
calculate the quartile.
**There are a number of choices.**
1. Show that the set of all polynomials of deg=2 is not a vector
space over reals.
can this be fixed, can we have a set of polynomials that is a
vector space over reals?
2. Show that the set of 2x2 matrices with m_22 = 1 is not a
vector space over reals.
3. Show that the set of infinitely-differentiable real functions
is a a vector space under pointwise function addition, and
pointwise scalar multiplication as defined in class,...