this homework question #4 please
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![4. Write pseudo- e to randomly choose k of n values in an array A[] so that they
are in the random chosen values are in the first k positions.
5. Distributions
(a) Write down the formula for the density of the exponential distribution.
(b) What does it mean that a random variable coming from an exponential has
no memory?
(c) Prove that an exponentially distributed random variable has no memory.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F33eba9e5-eb7d-44a1-93e3-ed0ee897e17f%2Fa50ed619-9afa-450f-9cfd-8417cbe7fec1%2Fy0nww8_processed.jpeg&w=3840&q=75)
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- suppose a computer solves a 100x100 matrix using Gauss elimination with partial pivoting in 1 second, how long will it take to solve a 300x300 matrix using Gauss elimination with partial pivoting on the same computer? and if you have a limit of 100 seconds to solve a matrix of size (N x N) using Gauss elimination with partial pivoting, what is the largest N can you do? show all the steps of the solutionfor linear algebra in solving a sytem of linear equations in form AX = B. True or false. 1.the array of unknown x be the same size as array of constants in B 2. the number of rows of A must be the same as rows of B 3. A must have the same number of columns as rows 4. Number of columns in A must be the same as number of rows in BIn Matlab practice matrix operations with for loops. Create a random matrix 10*10 in size, e.g. A=rand(10); Then use two for loops (nested for loops) to “survey” each element in each column and row and do the following operations: (a) Add all the elements together; (b) When the element is smaller than 0.5, set it to zeros; When the element is larger or equal to 0.5, set it to ones.
- I. Fermat's test consists of using Fermat's Theorem (an¹=1 (mod n)) with prime n. Just pick any number a E {1, ..., n-1} and check if it satisfies the expression. If not, then it must be a composite number, that is, it is not prime. II. Although Fermat's Theorem is used to check whether a number is prime or not, we can still obtain equality (an¹-1 (mod n)) even when n is not prime. E The numbers for which this situation occurs are called Carmichael numbers or pseudoprimes. III. Both the Miller-Rabin and AKS algorithms (checking a prime number) work for any type of input and are polynomial time. However, only AKS is deterministic. IV. The Miller-Rabin algorithm guarantees when a number is prime, but when it is composite (non-prime) it can only guarantee this characteristic in probabilistic terms. Only the following items are correct: A I, II, III B I, II, IV C I, III, IV D II, III, IV E I, II, III, IVUSING PYTHON A tridiagonal matrix is one where the only nonzero elements are the ones on the main diagonal (i.e., ai,j where j = i) and the ones immediately above and belowit(i.e.,ai,j wherej=i+1orj=i−1). Write a function that solves a linear system whose coefficient matrix is tridiag- onal. In this case, Gauss elimination can be made much more efficient because most elements are already zero and don’t need to be modified or added. Please show steps and explain.Write a program that does the following: 1- Ask the user to enter the number of variables on a Linear- System 2- Ask the user to enter matrix elements 3- Ask the user enter vector elements 4- Ask the user to enter initial approximation for the solution 5- Solve the linear-system using Jacobi iteration and show the results and number of iterations needed 6- Solve the linear-system using Gauss-Seidel iteration and show the results and number of iterations needed 7- Show which of the two methods is better
- Q2/ Simplify using K- map for the following : Simplify the Boolean function F(A, B, C, D, E) = (0, 2, 4, 6, 9, 13, 21, 23, 25, 29, 31) %3DTwo small charged objects attract each other with a force F when separated by a distance d.If the charge on each object is reduced to one-fourth of its original value and the distance between them is reduced to d/2,the force becomes?In matlab can you please show me a code that can output the given matrices? use matrix operation :D any code except for this one "K = [4 3 2 1;5 14 13 12;6 15 16 11;7 8 9 10]"
- let X = {0, 1}1. Given the function, f(A, B, C, D,E) = E m(prime number:"5 input variables that generates output 1 if and only if the number of l's in the input is prime number"), minimize it using the Karnaugh map method.3 : Prove that the sum of the three variables of the sum exponent f(x) = Σe is strictly convex. For this i=1 purpose, compute the Hessian matrix of the function f(x).