2. Consider the given seven symbols with probabilities as {A, B,
C, D, E, F, G}...
2. Consider the given seven symbols with probabilities as {A, B,
C, D, E, F, G} = {0.25, 0.20, 0.18, 0.15, 0.12, 0.06, 0.04}. Use
Huffman coding to determine coding bits, entropy and average bits
per symbol. Verify the same with Matlab . Verify the same
with Matlab .Verify the same with Matlab ( very importent )
.
2. Define a relation R on pairs of real numbers as follows: (a,
b)R(c, d) iff...
2. Define a relation R on pairs of real numbers as follows: (a,
b)R(c, d) iff either a < c or both a = c and b ≤ d. Is R a
partial order? Why or why not? If R is a partial order, draw a
diagram of some of its elements.
3. Define a relation R on integers as follows: mRn iff m + n is
even. Is R a partial order? Why or why not? If R is...
let us create a variable for a row vector a = [1, 4, 1, 3, 2,...
let us create a variable for a row vector a = [1, 4, 1, 3, 2, 5,
0] and calculate the mean value of its elements using the Matlab
function ‘mean’ and store this value in variable aMean. Fig. 1
gives the Matlab code to do this.
a = [1, 4, 1, 3, 2, 5, 0];
aMean = mean(a);
Figure 1: Matlab code – row vector and mean of its elements.
Let us now construct a row vector b that...
Suppose X and Y are independent Geometric random variables, with
E(X)=4 and E(Y)=3/2.
a. Find the...
Suppose X and Y are independent Geometric random variables, with
E(X)=4 and E(Y)=3/2.
a. Find the probability that X and Y are equal,
i.e., find P(X=Y).
b. Find the probability that X is strictly
larger than Y, i.e., find P(X>Y). [Hint: Unlike Problem 1b, we
do not have symmetry between X and Y here, so you must
calculate.]
Let the population have N=7 units, with {(unit,value)} =
{(A,-1),(B,+1),(C,-2),(D,+3),(E,-4),(F,+5),(G,-6)}. The design is
as follows: first...
Let the population have N=7 units, with {(unit,value)} =
{(A,-1),(B,+1),(C,-2),(D,+3),(E,-4),(F,+5),(G,-6)}. The design is
as follows: first choose A or B at random; if A then choose from
{C,D} at random, if B then choose from {E,F,G} at random. 1) Find
the first-order inclusion probabilities (note that the sample size
n is fixed at 2).
Verify (show numerically for this example) that the
Horvitz-Thompson estimator is unbiased for the population total.
(Hint: find the probability of each sample and the value...
Group A observations are 1, 2, 3; group B observations are 3, 4,
5; group C...
Group A observations are 1, 2, 3; group B observations are 3, 4,
5; group C observations are 5, 6, 7. Make a table of these
observations with each group as a column. Perform a one-way ANOVA
test. What is the null hypothesis? Calculate each term of the ANOVA
table (e.g., compute the sum of squares, degrees of freedom). What
is the F-statistic? If a = .05, what is the result of your
hypothesis test?