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bearhunter [10]
3 years ago
8

. A binary string containing M 0’s and N 1’s (in arbitrary order, where all orderings are equally likely) is sent over a network

. What is the probability that the first r bits of the received message contain exactly k 1’s?
Mathematics
1 answer:
Sophie [7]3 years ago
8 0

Answer:

P(k) = \frac{\binom{N}{k} \binom{(M+N) - N}{r-k}}{\binom{M+N}{r}}

Step-by-step explanation:

We can model the string as a hypergeometric distribution, as each bit has two possible values, 1 or 0, and the chance of a 1 or 0 changes with every bit, as there are a finite number M of 0's and N of 1's and every bit takes one of those values.

If M+N (total size of the string) >> r (number of trials), we could model it as a binomial distribution as the probability of a 1 or 0 wouldn't change in a significant amount with every bit, but as we don't know the magnitude of M+N and r, we follow up with hypergeometric distribution.

The distribution has the following formula for probability:

P(k) = \frac{\binom{K}{k} \binom{N - K}{n-k}}{\binom{N}{n}}

Where k is the number of sucesses, K is how many total sucess states are in the population, N is the population size and n is the number of draws.

For our case, a 1 would be a sucess, i.e. k the number of 1's we want to know the probability, N our total number of 1's, M+N the length of the string (population size) and we want to analyse what happens in the first r bits (number of draws):

P(k) = \frac{\binom{N}{k} \binom{(M+N) - N}{r-k}}{\binom{M+N}{r}}

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6x + 8 = 5x - 7 solve for x plssss
Elanso [62]

Answer:

6+8=5−7

6x+8=5x-76x+8=5x−7

6+8−8=5−7−8

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

Simplify

Subtract the numbers

Subtract the numbers

6=5−15

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

Subtract 

5

5x5x

 from both sides of the equation

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

6=5−15

6x=5x-156x=5x−15

6−5=5−15−5

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

Simplify

Combine like terms

Multiply by 1

Combine like terms

=−15

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

Solution

=−15

Step-by-step explanation:

<h2>ask me in brainlist answer please </h2>

6 0
2 years ago
Cushing's disease is characterized by muscular weakness due to adrenal or pituitary dysfunction. To provide effective treatment,
Katyanochek1 [597]

Answer:

Since the calculated value of t =-0.427 does not  fall in the critical region so we accept H0 and conclude that there is enough evidence to show that mean difference in the  age of onset of symptoms and age of diagnosis is  25 months  .

Step-by-step explanation:

The given data is

Difference d= -24 -12 -55 -15 -30 -60 -14 -21 -48 -12 -25 -53 -61 -69 -80

∑ d= -579

 ∑d²= 29871

1) Let the hypotheses be

H0: ud= 25 against the claim    Ha: ud ≠25

H0 : mean difference in the  age of onset of symptoms and age of diagnosis is  25 months  .

Ha:   mean difference in the  age of onset of symptoms and age of diagnosis is not 25 months.

 

2) The degrees of freedom = n-1= 15-1= 14

3) The significance level is 0.05

4) The test statistic is

t= d`/sd/√n

The critical region is ║t║≤ t (0.025,14) = ±2.145

d`= ∑di/n= -579/15= -38.6

Sd= 23.178  (using calculators)

Therefore

t= d`/ sd/√n

t= -38.6/ 23.178√15

t= -1.655/3.872= -0.427

5) Since the calculated value of t =-0.427 does not  fall in the critical region so we accept H0 and conclude that there is enough evidence to show that mean difference in the  age of onset of symptoms and age of diagnosis is  25 months  .

8 0
3 years ago
How many solutions does the linear system below have? -8x+2y=6 and -4x+y=3
Verizon [17]

Answer:

Step-by-step explanation:

Try dividing the first equation by 3.  The result will be identical to the second equation.  Thus, we have two lines that coincide, and therefore there are an infinite number of solutions.

7 0
2 years ago
For every $5 tent saved, his his dad will contribute $2 to his saving account. How much will Trent have to put into the account
KonstantinChe [14]

Answer:

  $40

Step-by-step explanation:

Trent contributes 5/(5+2) = 5/7 of the amount in his account. For an amount of $56, he must contribute ...

  (5/7)×$56 = $40

Trent will have to put $40 into the account before he can buy a $56 skateboard.

7 0
3 years ago
HELP ASAP!!!! simplify 3^2-4/5
My name is Ann [436]

Answer:

9-4/5

5/5 = 1

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
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