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

Find the 14th term in the arithmetic sequence. 60, Find the 14th term in t...

Find the 14th term in the arithmetic sequence. 60, 68, 76, 84, 92

Determine differential equation from direction field, Thus, just why do we ...

Thus, just why do we care regarding direction fields? Two nice pieces of information are there which can be readily determined from the direction field for a differential equation.

Calculate and plot the cdf of p-values, A discrete-valued random variable X...

A discrete-valued random variable X takes values in 0, 1, 2, . . . , where p(X = i) = π i. (a) Write down formulas for: the p-value at X = i the probability distributi

Regarding submitting sample work, How can I submit a sample of my work in e...

How can I submit a sample of my work in either teaching online or checking homework as I am retired and doing this for the first time?

High self-esteem helps learning-how do children learn?, High Self-esteem He...

High Self-esteem Helps Learning :  Consider Ajay, a student of Class 2. He is constantly told by his irritated father, "How stupid you are! You don't even understand this! Even yo

Series solution, Find the series solution of2x2y”+xy’+(x2-3)Y=0 about regul...

Find the series solution of2x2y”+xy’+(x2-3)Y=0 about regular singular point

Limits at infinity part ii, Limits At Infinity, Part II :  In this sectio...

Limits At Infinity, Part II :  In this section we desire to take a look at some other kinds of functions that frequently show up in limits at infinity.  The functions we'll be di

Calculate the acceleration time, Question A 22 kW, 3-phase, 415 V, 40 A,...

Question A 22 kW, 3-phase, 415 V, 40 A, 50 Hz, 960 rpm, 0.88 PF squirrel cage induction motor drives a pump. The total inertia of the drives system is 1.2 kg-m2. Determine th

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