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jeka94
2 years ago
12

An m-bit password is required to access a system. a hacker systematically works through all possible m-bit patterns. let x be th

e number of patterns tested until the correct password is found. find the conditional pmf of x given that the password has not been found after k tries
Mathematics
1 answer:
GREYUIT [131]2 years ago
5 0
<span>(a) Describe the underlying sample space S . Ans : Let a represent the correct m -bit pattern. Then S = { ( x 1 ,..., x n , a ) } (3) where x i 6 = a , i = 1 ,...,n , and n = 0 , 1 ,..., 2 m . The m -bit pattern x i is the i -th pattern tried by the hacker. So assuming he keeps track of the patterns tried, we also have that x i not equal to xj i.e i not equal to j ( b) Show the mapping from S to S X . Ans : The mapping is X (( x 1 ,..., x n , a )) = n + 1 , with S X = { 1 , 2 ,..., 2 m } (c) Find the PMF of X . Ans : For convenience, let A k = “ k -th attempt is correct”. Then p X ( n ) = P " A n n - 1 \ i =1 A c i # . It should be clear that p X (1) = P [ A 1 ] = 2 - m , since there are 2 m possible passwords, and the hacker tries them randomly. We also have p X (2) = P [ A 2 | A c 1 ] P [ A c 1 ] (4) = 1 2 m - 1 2 m - 1 2 m (5) = 1 = 2 m Similarly, p X (3) = P [ A 3 | A c 2 A c 1 ] P [ A c 2 | A c 1 ] P [ A c 1 ] (7) = 1 2 m - 2 2 m - 2 2 m - 1 2 m - 1 2 m (8) = 1 2 m . (9) Proceeding in this way, we quickly see that X is in fact uniformly distributed in S X = { 1 , 2 ,..., 2 m } . The average number of attempts needed to break an m -bit password is thus 2 m - 1 . For a typical password of ten 8-bit ASCII characters, i.e. 80 bits, it will take 2 79 = 6 . 04 × 10 23 attempts on average</span>
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Answer:

Binomial probability, with n = 5, p = 0.352

Step-by-step explanation:

For each time Mookie Betts went to bat, there were only two possible outcomes. Either he got a base-hit, or he did not. The probability of getting a hit on each at-bat is independent of any other at-bat. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

His average was 0.352.

This means that p = 0.352

Assume he has five times at bat tonight in the Red Sox-Yankees game.

This means that n = 5

a. This is an example of what type of probability

Binomial probability, with n = 5, p = 0.352

8 0
3 years ago
At a department store, Kendra has a debt greater than $25.00. Which could be Kendra’s balance?
jeka57 [31]
Debt is negative dollars, which means she owes at least 25 dollars to the department store

her balance is -25.00 + x

hope this helps

or -25 >x


5 0
3 years ago
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in an examination of 140 students, 80 students passed mathematics,65 passed physics, 75 passed chemistry, 33 passed mathematics
Olegator [25]

Answer:

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3 years ago
Ms jenkins has a grass lawn that is 24m wide and 30m long. mr jenkins cuts the grass at a reate of 9m per minute. how long will
Kisachek [45]

It will take Mr. Jenkins 1 hr and 20 minutes to cut all the grass.

To know how long it will take Mr. Jenkins to cut all the grass, get the total area of the lawn and divide it by the rate Mr. Jenkins cut the grass.

The area of the lawn can be calculated using the formula for the area of a rectangle given by:

A = l x w

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Using this formula, the grass lawn that is 24 m wide and 30 m long has an area of:

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Meanwhile, the time it will take Mr. Jenkins to cut the grass lawn with an area of 720 m^2 can be computed using the rate.

amount = rate x time

720 m^2 = 9 m^2/minute x t

t = 720 / 9

t = 80 minutes = 1 hr 20 minutes

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1 year ago
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n200080 [17]

Answer: 3/8

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