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.
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).
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.؟
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,...