Using the law of total probabilty Suppose we have a sample space S and two events A and B such that S= AUB and ANB=0 and an event E, Suppose we have the following results: . Р(4) — 1/3 • P(B) = 2/3 P(E|A) = 1 P(E|B) = 0 What is P(E) ?
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- Correct answer will be upvoted else downvoted. Computer science. You are given three positive (more prominent than nothing) integers c, d and x. You need to track down the number of sets of positive integers (a,b) with the end goal that balance c⋅lcm(a,b)−d⋅gcd(a,b)=x holds. Where lcm(a,b) is the most un-normal various of an and b and gcd(a,b) is the best normal divisor of an and b. Input The primary line contains one integer t (1≤t≤104) — the number of experiments. Each experiment comprises of one line containing three integer c, d and x (1≤c,d,x≤107). Output For each experiment, print one integer — the number of sets (a,b) to such an extent that the above uniformity holds.For all positive numbers aaand bbwith a>ba>b, ln(a−b)=ln(a)/ln(b)ln(a−b)=ln(a)/ln(b) True or falseGiven A = {1,2,3} and B={u,v}, determine. a. A X B b. B X B
- Let l be a line in the x-y plane. If l is a vertical line, its equation is x 5a for some real number a. Suppose l is not a vertical line and its slope is m. Then the equation of l is y 5mx 1b, where b is the y-intercept. If l passes through the point (x0, y0,), the equation of l can be written as y 2y0 5m(x 2x0 ). If (x1, y1) and (x2, y2) are two points in the x-y plane and x1 ≠ x2, the slope of line passing through these points is m 5(y2 2y1 )/(x2 2x1 ). Write a program that prompts the user two points in the x-y plane. The program outputs the equation of the line and uses if statements to determine and output whether the line is vertical, horizontal, increasing, or decreasing. If l is a non-vertical line, output its equation in the form y 5mx 1b.please try to simulate the probability of rolling a Die with Sample Space* S={1,2,3,4,5,6} and the probability of each sample point has a 1/6 chance of occurring, i.e., you need to verify that your simulation converges to 1/6 when you select one point of sample space. When X is a random variable for sample point of rolling a Die, Pr(X<=4)=2/3. Please verify this result by simulation. Please let me know how to make an Excel file as stated above.Let l be a line in the x-yplane. If l is a vertical line, its equation is x = a for some real number a. Suppose l is not a vertical line and its slope is m. Then the equation of l is y = mx + b, where b is the y-intercept. If l passes through the point (x₀, y₀), the equation of l can be written as y - y₀ = m(x - x₀). If (x₁, y₁) and (x₂, y₂) are two points in the x-y plane and x₁ ≠ x₂, the slope of line passing through these points is m = (y₂ - y₁)/(x₂ - x₁). Instructions Write a program that prompts the user for two points in the x-y plane. Input should be entered in the following order: Input x₁ Input y₁ Input x₂
- • Simplify the Boolean functions by means of the tabulation matching method: a. F(w,x,y,z) = Σm(2,3,12,13,14,15) b. P(m,n,o,p,q,r) =Em(6,9,13,18,19,25,27,29,41,45,57,61) c. P(A,B,C,D,E,F,G) =Σm(20,28,38,39,52,60,102,103)You are given a N*N maze with a rat placed at maze[0][0]. Find whether any path exist that rat can follow to reach its destination i.e. maze[N-1][N-1]. Rat can move in any direction ( left, right, up and down).Value of every cell in the maze can either be 0 or 1. Cells with value 0 are blocked means rat cannot enter into those cells and those with value 1 are open.Input FormatLine 1: Integer NNext N Lines: Each line will contain ith row elements (separated by space)Output Format :The output line contains true if any path exists for the rat to reach its destination otherwise print false.Sample Input 1 :31 0 11 0 11 1 1Sample Output 1 :trueSample Input 2 :31 0 11 0 10 1 1Sample Output 2 : false Solution: //// public class Solution { public static boolean ratInAMaze(int maze[][]){ int n = maze.length; int path[][] = new int[n][n]; return solveMaze(maze, 0, 0, path); } public static boolean solveMaze(int[][] maze, int i, int j, int[][] path) {//…Given is a strictly increasing function, f(x). Strictly increasing meaning: f(x)< f(x+1). (Refer to the example graph of functions for a visualization.) Now, define an algorithm that finds the smallest positive integer, n, at which the function, f(n), becomes positive. The things left to do is to: Describe the algorithm you came up with and make it O(log n).
- Generate 100 synthetic data points (x,y) as follows: x is uniform over [0,1]10 and y = P10 i=1 i ∗ xi + 0.1 ∗ N(0,1) where N(0,1) is the standard normal distribution. Implement full gradient descent and stochastic gradient descent, and test them on linear regression over the synthetic data points. Subject: Python ProgrammingThe DFA M = ({qo,, 95}, E, 6, 90, 91, 95}) with = {0, 1} is given by this table for the transition function 8. 80 90 * 91 92 90 95 92 92 94 91 93 93 94 94 94 91 *95 95 94 (a) Draw a transition diagram of M. Cross out any state(s) that we don't need. Now partition the set of states into two parts such that it is immediately clear that no state in the first set is equivalent to a state in the second set. (b) Find a minimum DFA equivalent to M.Let L={(a, b)|a, b∈Z,(a−b) mod 4 = 0}. We want to program a robot that can get to each point (x, y)∈L starting at (0,0). (a)Give an inductive definition of L. This will describe the steps you want the robot to take to get to points in L starting at (0,0). Let L′ be the set obtained by your inductive definition. (b)Prove inductively that L′⊆L, i.e., every point that the robot can get to is in L. (c)Prove that L⊆L′, i.e., the robot can get to every point in L. To prove this, you need to give the path the robot would take to get to every point in L from (0,0), following the steps defined by your inductive rules.