1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Bas_tet [7]
2 years ago
5

A source of information randomly generates symbols from a four letter alphabet {w, x, y, z }. The probability of each symbol is

as follows: P(w) = 1 2 ; P(x) = 1 4 ; P(y) = 1 8 ; and P(z) = 1 8 . These symbols are now encoded into binary codes using the scheme shown below. Let the random variable L denote the length of the binary code and pL(l) denote the PMF of L.symbol codew 0x 10y 110z 111Find the expectation and variance of L.
Mathematics
1 answer:
koban [17]2 years ago
5 0

The expected length of code for one encoded symbol is

\displaystyle\sum_{\alpha\in\{w,x,y,z\}}p_\alpha\ell_\alpha

where p_\alpha is the probability of picking the letter \alpha, and \ell_\alpha is the length of code needed to encode \alpha. p_\alpha is given to us, and we have

\begin{cases}\ell_w=1\\\ell_x=2\\\ell_y=\ell_z=3\end{cases}

so that we expect a contribution of

\dfrac12+\dfrac24+\dfrac{2\cdot3}8=\dfrac{11}8=1.375

bits to the code per encoded letter. For a string of length n, we would then expect E[L]=1.375n.

By definition of variance, we have

\mathrm{Var}[L]=E\left[(L-E[L])^2\right]=E[L^2]-E[L]^2

For a string consisting of one letter, we have

\displaystyle\sum_{\alpha\in\{w,x,y,z\}}p_\alpha{\ell_\alpha}^2=\dfrac12+\dfrac{2^2}4+\dfrac{2\cdot3^2}8=\dfrac{15}4

so that the variance for the length such a string is

\dfrac{15}4-\left(\dfrac{11}8\right)^2=\dfrac{119}{64}\approx1.859

"squared" bits per encoded letter. For a string of length n, we would get \mathrm{Var}[L]=1.859n.

You might be interested in
If you knew that the vertical intercept for a straight line was 15, that the slope was -.5, and that the independent variable ha
Finger [1]
Y=-.5x+15 plug in 8 for x and you get 11
7 0
2 years ago
In 56.0183 which digit is in the tens place?
notka56 [123]

Answer:

The digit that is in the TENS place is 5

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
These are samples of student work. Both students got the same answer, but did the work differently. Which student did the work c
Alchen [17]

Answer:

Student B did the problem corectly

Step-by-step explanation:

Student a did 3*4 while student B did 3*3*3*3 which would equal 27

3 0
2 years ago
What is 93+(68+7) property
allochka39001 [22]
The associative property states a + (b + c) = (a + b) + c

So your answer is associative property.

4 0
3 years ago
25 Points!!! Help plzz!! Will give Brainliest!!!
Lady_Fox [76]

Answer:

Option C : ASA

Step-by-step explanation:

Side WS Lies between ∠W and ∠S

Side NT lies between ∠N and ∠T

Hence the theorem which supports the congruency  of the two triangles

is ASA

Angle - Side - Angle

3 0
2 years ago
Other questions:
  • 8 please this is due tomorrow and I really need it I will give brainliest answer=)))))))):))))))
    8·1 answer
  • Katrina had 7/8 of a candy bar she gave 2/3 of it to her brother how much of the Candy bar did Katrina have left
    7·1 answer
  • What is a fraction eqivalent to 5/6​
    8·2 answers
  • 22 gallons of gas cost $65.56. What is the unit rate for 1 gallon of gas?
    8·2 answers
  • What is the area of a rectangle that is ​2 ​ ​1 ​​ centimeter ​wide and ​5 ​ ​3 ​​ centimeter long? ​​
    14·1 answer
  • For every 15 seventh graders in band, there are 20 eighth graders. What is the ratio of eighth graders to seventh graders?
    15·1 answer
  • A standard deck of has 52 cards, and contains 13 cards of each of the four suits: diamonds, spades, hearts, and clubs. What is t
    14·1 answer
  • Simplify the expression using the order of operations show all your work 150- (4²+4) ÷ 2
    11·1 answer
  • For the function f(x) = 2x - 11, what is the average rate of change over the interval -1 ≤ x ≤ 1? average rate of change:​
    7·1 answer
  • There are 10 mm in one cm and 100 cm in 1m. an adult alligator is about 4,000 mm long and an adult crocodile is abt 6m long
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!