1. Use the binomial theorem to show i) Ek_0 () = 21; ii) _o(-1)* (m.) =...
Please show lots of detailed work. Thank you. Exercise 2.5. Use the Binomial Theorem to prove that, for all n 20 and for all x e R, Hint: Set y 1 in Theorem 2.2.8 and then differentiate. Exercise 2.6. Use the result of the previous exercise to find the value of the sum + 2 + 10 10
Show all work and steps! 1-Answer the following questions about conditional probability and Bayes theorem a. You roll 2 dice and record the sum i. ii. iii. Write the sample space What is the probability of the sum being 10? What is the probability that at least one of the die values was a 6 given that the sum was greater than or equal to 7?
An m×n array A of real numbers is a Monge array if for all i,j,k, and l such that 1≤i<k≤m and 1≤j<l≤n , we have >A[i,j]+a[k,l]≤A[i,l]+A[k,j]> In other words, whenever we pick two rows and two columns of a Monge array and consider the four elements at the intersections of the rows and columns, the sum of the upper-left and lower-right elements is less than or equal to the sum of the lower-left and upper-right elements. For example, the following...
Please show all work and steps !! 1. Answer the following questions about conditional probability and Bayes theorem a. You roll 2 dice and record the sum i. ii. iii. Write the sample space What is the probability of the sum being 10? What is the probability that at least one of the die values was a 6 given that the sum was greater than or equal to 7?
3 Problem 3 Use Stokes' Theorem to find the circulation of F(x, y, z) = 6yi + 4xj + z?k counter- clockwise around the ellipse 4.x2 + 25y2 = 1. Hint: I am allowing you to take for granted that the area inside this ellipse is to so put that to use in turning this problem into a double integral of the k-component of the curl over the region inside the ellipse.
please use octave calculator or matlab to answer (a)(ii)and(iii) 2. (a) Use Octave as a Calculator1 to answer this question. Suppose that A and B are two 8 × 9 matrices. The (i, j)-entry of the matrix B is given by i *j -1. The (i, j)-entry of the matrix A equals 0 if i + j is divisible by 5 and equals the (i, j)-entry of the matrix B otherwise. i. What are the rank and nullity of matrices...
Question 1 a. Define the following matrices in a script file (M-file), ? = ( 8 9 10 11; 23 9 16 15 ;11 12 3 6; 1 2 8 9 ) ? = ( 2 21 7 15; 12 4 8 22; 23 9 5 13; 23 4 21 22) ℎ = (4 9 12 15) b. Add suitable lines of codes to the M-file to do the following. Each of the following points should be coded in only...
Prove the Binomial Theorem, that is Exercises 173 (vi) x+y y for all n e N C) Recall that for all 0rS L is divisible by 8 when n is an odd natural number vii))Show that 2 (vin) Prove Leibniz's Theorem for repeated differentiation of a product: If ande are functions of x, then prove that d (uv) d + +Mat0 for all n e N, where u, and d'a d/v and dy da respectively denote (You will need to...
Due in 2 hr (a) Use Octave as a Calculator to answer this question Suppose that A and B are two 8 × 9 matrices. The (i, j)-entry of the matrix B is given by i *j -1. The (i,j)-entry of the matrix A equals 0 if i +j is divisible by 5 and equals the (i,j)-entry of the matrix B otherwise. i. What are the rank and nullity of matrices A and B? Is vector u =[964,-71,4249, 59, 234,-196.97]...
please answer questions #7-13 7. Use a direct proof to show every odd integer is the difference of two squares. [Hint: Find the difference of squares ofk+1 and k where k is a positive integer. Prove or disprove that the products of two irrational numbers is irrational. Use proof by contraposition to show that ifx ty 22 where x and y are real numbers then x 21ory 21 8. 9. 10. Prove that if n is an integer and 3n...