(c) Determine the probability that the number chosen at random is either a multiple of 47 or a multiple of 23.
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2. Suppose an integer is chosen at random from the set S of the first 2510 positive integers that is, from the set S- [...
Assume that a student is chosen at random from a class. Determine whether the events A...
Assume that a student is chosen at random from a class. Determine whether the events A and B are independent, mutually exclusive, or neither. A: The student is a full-time student. B : The student is a part-time student. Select the correct answer i. The events A and B are independent. ii. The events A and B are mutually exclusive. ili. The events A and B are neither independent nor mutually exclusive. The correct answer is:
2. Let n be a positive integer. Denote the number of positive integers less than n and rela- tive...
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...
Problem 2. Choose an integer at random from -3 to 6. The event A occurs if...
Problem 2. Choose an integer at random from -3 to 6. The event A occurs if the chosen number is even, B occurs if the chosen number is smaller than 3; and C occurs if the chosen number is larger than 8. (a) List all the outcomes in Ω and in the events A, B and C. (b) Determine A', AUB, AG, A B, (c) Is A С B? Is B A? Are A and B mutually er clusive? (d)...
1) (a) (14 pts.) Consider the experiment in which a number is chosen uniformly in (1;...
1) (a) (14 pts.) Consider the experiment in which a number is chosen uniformly in (1; 2; : : : ; 10). Let event A be the number is divisible by 3, and event B be the number is (strictly-) greater than 5. (i) Write the sample space S for the aforementioned experiment and express events A and B as subsets of S. (ii) Are A and B mutually exclusive? Prove. (iii) Are A and B statistically independent? Prove.
3. (a) A fair dice is tossed 6 times. Suppose A is the event that the...
3. (a) A fair dice is tossed 6 times. Suppose A is the event that the number of occurrences of an even digit equals the number of occurrences of an odd digit, while B is the event that at most three odd digits will occur i. Determine with reason if the events A and B are mutually exclusive. ii. Determine the probabilities of the events A and B. Are the events A and B independent? b) Suppose a fair coin...
Let ? be a positive integer random variable with PMF of the form ??(?)=12⋅?⋅2−?,?=1,2,…. Once we...
Let ? be a positive integer random variable with PMF of the form ??(?)=12⋅?⋅2−?,?=1,2,…. Once we see the numerical value of ?, we then draw a random variable ? whose (conditional) PMF is uniform on the set {1,2,…,2?}. 1.1 Write down an expression for the joint PMF ??,?(?,?). For ?=1,2,… and ?=1,2,…,2?: ??,?(?,?)=? 1.2 Find the marginal PMF ??(?) as a function of ?. For simplicity, provide the answer only for the case when ? is an even number. (The...
Problem 2. Let n be a positive integer. We sample n numbers ai,...,an from the set...
Problem 2. Let n be a positive integer. We sample n numbers ai,...,an from the set 1, 2,...,n} uniformly at random, with replacement. Say that the picks i and j with i < j are a match if a -aj. What is the expected total number of matches? Hint: Use indicators. Wİ
3. A computer chooses 100 independent random numbers, each uniformly from the set of integers between...
3. A computer chooses 100 independent random numbers, each uniformly from the set of integers between 1 and 200. What is the expected value of: (a) The number of the chosen numbers which are multiples of 10
6. Determine whether each of the following is true or false (note: the statement is true...
6. Determine whether each of the following is true or false (note: the statement is true if it is always true, otherwise it is false). If you say it is true then refer to a known result or give a proof, while if you say it is false then give a counterexample, i.e., a particular case where it fails. (a) If A, B and C are independent, the Pr(AlBnc)- Pr (A) (b) The events S., A are independent (S is...
According to a magazine, people read an average of more than three books in a month....
According to a magazine, people read an average of more than three books in a month. A survey of 25 random individuals found that the mean number of books they read was 2.9 with a standard deviation of 1.22. a. To test the magazine's claim, what should the appropriate hypotheses be? b. Compute the test statistic. c. Using a level of significance of 0.05, what is the critical value? d. Find the p-value for the test. e. What is your...
Assume that a student is chosen at random from a class. Determine whether the events A and B are independent, mutually exclusive, or neither. A: The student is a full-time student. B : The student is a part-time student. Select the correct answer i. The events A and B are independent. ii. The events A and B are mutually exclusive. ili. The events A and B are neither independent nor mutually exclusive. The correct answer is:
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...
Problem 2. Choose an integer at random from -3 to 6. The event A occurs if the chosen number is even, B occurs if the chosen number is smaller than 3; and C occurs if the chosen number is larger than 8. (a) List all the outcomes in Ω and in the events A, B and C. (b) Determine A', AUB, AG, A B, (c) Is A С B? Is B A? Are A and B mutually er clusive? (d)...
3. (a) A fair dice is tossed 6 times. Suppose A is the event that the number of occurrences of an even digit equals the number of occurrences of an odd digit, while B is the event that at most three odd digits will occur i. Determine with reason if the events A and B are mutually exclusive. ii. Determine the probabilities of the events A and B. Are the events A and B independent? b) Suppose a fair coin...
Problem 2. Let n be a positive integer. We sample n numbers ai,...,an from the set 1, 2,...,n} uniformly at random, with replacement. Say that the picks i and j with i < j are a match if a -aj. What is the expected total number of matches? Hint: Use indicators. Wİ
3. A computer chooses 100 independent random numbers, each uniformly from the set of integers between 1 and 200. What is the expected value of: (a) The number of the chosen numbers which are multiples of 10
6. Determine whether each of the following is true or false (note: the statement is true if it is always true, otherwise it is false). If you say it is true then refer to a known result or give a proof, while if you say it is false then give a counterexample, i.e., a particular case where it fails. (a) If A, B and C are independent, the Pr(AlBnc)- Pr (A) (b) The events S., A are independent (S is...
According to a magazine, people read an average of more than three books in a month. A survey of 25 random individuals found that the mean number of books they read was 2.9 with a standard deviation of 1.22. a. To test the magazine's claim, what should the appropriate hypotheses be? b. Compute the test statistic. c. Using a level of significance of 0.05, what is the critical value? d. Find the p-value for the test. e. What is your...
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