Suppose that two integers from the set of 8 integers {1, 2, … , 8} are...

Suppose that two integers from the set of 8 integers {1, 2, … , 8} are choosen at random. Find the probability that

5 and 8 are picked.

Both numbers match.
Sum of the two numbers picked is less than 4.

[3+3+4 marks] Suppose that you pick a bit string from the set of all bit strings of length ten. Find the probability that:

The bit string has the sum of its digits equal to seven.
The bit string has more 0s than 1s.

The bit string has exactly two 1s, given that the string begins with a 1

Expert Solution

orchestra answered 2 years ago

Suppose we are given a set ? containing 2? integers, and we wish to partition it...

Suppose we are given a set ? containing 2? integers, and we wish to partition it into two sets ?1 and ?2 so that |?1 | = |?2 | = ? and so that the sum of the numbers in ?1 is as close as possible to the sum of those in ?2. Let the neighborhood ? be determined by all possible interchanges of two integers between ?1 and ?2. Is ? exact?

Consider the following two sample data sets. Set 1: 5 3 2 8 6 Set 2:...

Consider the following two sample data sets. Set 1: 5 3 2 8 6 Set 2: 3 12 13 2 7 a. Calculate the coefficient of variation for each data set. b. Which data set has more variability? a. The coefficient of variation for set 1 is nothing %. (Round to one decimal place as needed.)

Consider the set of integers A = {1, 2, 3, 4, 5}. Pairs of numbers are...

Consider the set of integers A = {1, 2, 3, 4, 5}. Pairs of numbers are constructed where each number of the pair comes from set A. Construct the sampling distribution of sample ranges. Apply the Empirical Rule to this distribution.

Consider the integers from 1 to 10. Give the set of pairs (a, b) that corresponds...

Consider the integers from 1 to 10. Give the set of pairs (a, b) that corresponds to relation a ≡ b mod 1.

Suppose you receive utility ?(?, ?) = 8? 1/2 + ? from ? Instagram “likes” and...

Suppose you receive utility ?(?, ?) = 8? 1/2 + ? from ? Instagram “likes” and l minutes worked. Assume it takes 2 minutes to find an Instagram post to like, and you have 60 minutes to spend on work or Instagram. Assume your goal is to maximize your utility. a) How many Instagram posts will you like? How many minutes will you work? b) What is your total utility if you make the optimal choices above? c) Suppose the...

1.Suppose n and k are two positive integers. Pick a uniformly random lattice path from (0,...

1.Suppose n and k are two positive integers. Pick a uniformly random lattice path from (0, 0) to (n, k). What is the probability that the first step is ‘up’?

The Fibonacci sequence is the series of integers 0, 1, 1, 2, 3, 5, 8, 13,...

The Fibonacci sequence is the series of integers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 . . . See the pattern? Each element in the series is the sum of the preceding two elements. Here is a recursive formula for calculating the nth number of the sequence: Fib(N) = {N, if N = 0 or 1 Fib(N - 2) + Fib(N - 1), if N > 1 a) Write a recursive method fibonacci that returns...

1. "Give an example of a function that is defined on the set of integers that...

1. "Give an example of a function that is defined on the set of integers that is not a one-to-one function." Keep in mind that the above domain must be the set of integers. Identify what your codomain is, too. 2. "Give an example of a function that is defined on the set of rational numbers that is not an onto function." The above domain must be the set of rational numbers. Identify what your codomain is, too. This is...

1) a) From the set {-8, -2/3, 5i, √(-9), √2, 0, 3+3i, -2.35, 7} i) List...

1) a) From the set {-8, -2/3, 5i, √(-9), √2, 0, 3+3i, -2.35, 7} i) List the set of Natural Numbers ii) List the set of Integers iii) List of the set of Rational Numbers vi) List the set of Real Numbers b) i) -30 ÷ -6 - (-12 + 8) – 4 x 3 = ii) 10(-2) - (-6)4 (-10) – 6(-3) = (4, 4 marks) 2) a) 12/5 x...

1. The following set of data is from a sample of n = 8 171...

1. The following set of data is from a sample of n = 8 171 169 158 164 158 135 150 141 a) Find the mean, median, and mode. b) Calculate the variance, standard deviation, range, inter-quartile range, and coefficient of variation. c) Describe the shape of the data. d) List the five-number summary and build a boxplot.

Question