Determine randomly generated bit string, Mathematics

Assignment Help:

Assume E is the event that a randomly generated bit string of length 4 starts with a 1 and F is the event that this bit string consists of an even number of 1's. Are E and F independent if the 16 bit strings of length 4 are equally likely? 

Ans: Number of 4 bit strings that starts with 1 is 8, thus P(E) = .5  

Number of 4-bit string comprising even number of 1's is also 8 [C (4, 0) + C(4, 2) + C(4, 4)]. Hence P(F) = .5  

Here now Number of 4-bit string that begins with 1 and consists of even number of 1's is 4 [1 + C(3, 0)]. So P (E∩F) = .25.

Obviously P (E∩F) = P(E)*P(F). So E and F are independent.


Related Discussions:- Determine randomly generated bit string

Estimation of difference among two means, Estimation of difference among tw...

Estimation of difference among two means We know that the standard error of a sample is given by the value of the standard deviation (σ) divided by the square root of the numbe

Quadratic Equation, Short Cuts for solving quadratic equations

Short Cuts for solving quadratic equations

Linear Programming, describe phases of operations research study ?

describe phases of operations research study ?

Rounding, what is the nearest ten thousand of 92,892?

what is the nearest ten thousand of 92,892?

staticis, a statisics professor plans classes so carefully that the length...

a statisics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 46.0 and 56.0 minutes. find the probability that a given class pe

How many relations are possible from a set, How many relations are possible...

How many relations are possible from a set A of 'm' elements to another set B of 'n' elements?     Ans: A relation R from a set A to other set B is specified as any subset of A

What was the total cost of her order, Leslie ordered a slice of pizza for $...

Leslie ordered a slice of pizza for $1.95, a salad for $2.25, and a soda for $1.05. What was the total cost of her order? The cost of every item must be added together; $1.95 +

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd