Let n be an even positive integer. What is the probability that a randomly chosen n-bit string has the same number of zeros and ones? (Please show work)
Let n be an even positive integer. What is the probability that a randomly chosen n-bit string ha...
A 3-digit positive integer N is randomly chosen. Compute the probability of the event that (a) N is divisible by 3. (b) N is divisible by 3 if its leftmost digit is 1.
Imprecise Counting - Long Runs in Binary Strings Let n=2^k for some positive integer k and consider the set Sn of all n-bit binary strings. Let c be an integer in {0,…,n−k}. Consider any j∈{1,…,n−k−c+1}. How many strings b1,…,bn∈Sn have bj,bj+1,…,bj+k+c−1=00…0? In other words, how many strings in Sn have k+c consecutive zeros beginning at position j? For each j∈{1,…,n−k+c+1}, let Xj be the subset of Sn consisting only of the strings counted in the previous question. Show that (n−k−c+1)∑(j=1)...
I randomly pick two integers from 1 to n without replacement (n a positive integer). Let X be the maximum of the two numbers. (a) Find the probability mass function of X. (b) Find E(X) and simplify as much as possible (use formulas for the sum and sum of squares of the first n integers which you can find online).
Show that every positive integer n, there is a string of n consecutive integers where first integer is even, the second is divisible by a perfect square(other than 1), the third by a perfect cube(other than 1), etc..., and the nth is divisible by the nth power of an integer(other than 1). Then find an example for n = 3.
5 numbers chosen randomly without replacement. "B" represents number of even numbers, this random variable has this probability: x 0 1 2 3 4 5 p(B=x) 0.02693 0.15989 .33858 .31977 .13464 .02020 number of odd #s chosen would then be 5-x, if x is even #s chosen. "C" represents difference b/w # of even and # of odd chosen, --> C= 2B-5 a. probability that exactly 1 even # chosen? b. probability at most 1 even # chosen? c. prob....
number thoery
just need 2 answered
2. Let n be a positive integer. Denote the number of positive integers less than n and rela- tively prime to n by p(n). Let a, b be positive integers such that ged(a,n) god(b,n)-1 Consider the set s, = {(a), (ba), (ba), ) (see Prollern 1). Let s-A]. Show that slp(n). 1. Let a, b, c, and n be positive integers such that gcd(a, n) = gcd(b, n) = gcd(c, n) = 1 If...
2. Suppose an integer is chosen at random from the set S of the first 2510 positive integers that is, from the set S- [1,2,3,...,2510). Let A be the event that the number chosen is a multiple of 47. Let B be the event that the number chosen is a multiple of 23. (a) Determine with reason whether the events A and B are mutually exclusive. (b) Determine with reason whether the events A and B are independent (c) Determine...
What is the probability that a randomly chosen four letter word will begin with HA
I got a C++ problem.
Let n be a positive integer and let S(n) denote the number of divisors of n. For example, S(1)- 1, S(4)-3, S(6)-4 A positive integer p is called antiprime if S(n)くS(p) for all positive n 〈P. In other words, an antiprime is a number that has a larger number of divisors than any number smaller than itself. Given a positive integer b, your program should output the largest antiprime that is less than or equal...