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

Sets, creative assignment about sets

creative assignment about sets

If tan2x.tan7x=1 , tan9x = (tan7x + tan2x)/(1 - tan7x*tan2x) here its give...

tan9x = (tan7x + tan2x)/(1 - tan7x*tan2x) here its given 1 - tan2x*tan7x= 0 implies tan9x = infinity since tan9x = (3tan3x - tan^3(3x))/(1 - 3tan^2 (3x)) = infinity implies

Volume, Rajun uses 2/3 of a carton of milk to make a pancake. The volume of...

Rajun uses 2/3 of a carton of milk to make a pancake. The volume of milk he uses is 800ml. calculate the volume, in l, of a milk in carton?

Linear probability model, Pepsi:               A dummy variable where 1 den...

Pepsi:               A dummy variable where 1 denotes choice of Pepsi by the i-th customer and 0 otherwise Price_P:           The price of a 2-liter bottle of Pepsi at the time

Curvature - three dimensional space, Curvature - Three Dimensional Space ...

Curvature - Three Dimensional Space In this part we want to briefly discuss the curvature of a smooth curve (remind that for a smooth curve we require → r′ (t) is continuou

Concrete operational stage, Concrete Operational Stage :  Piaget describes...

Concrete Operational Stage :  Piaget describes a five-year-old boy playing with a collection of pebbles. First, he laid them in a line and counted along the line from left to righ

Shares and dividend, a man in rested rupee 800 is buying rupee 5 shares and...

a man in rested rupee 800 is buying rupee 5 shares and then are selling at premium of rupee 1.15. He sells all the shares.find profit

Devision, how many times can u put 10000 into 999999

how many times can u put 10000 into 999999

Fracrions, how do u do fractions on a nummber line

how do u do fractions on a nummber line

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