Publications by Ashish Kumar
data-605-week9-Discussion
data-605-week9-Discussion Ashish Kumar 03/23/2020 CHAPTER 9. CENTRAL LIMIT THEOREM Exercise 10 Page 339 Find the probability that among 10,000 random digits the digit 3 appears not more than 931 times. Solution n <- 100000 # Num of simulations trial <- rep(0, n) for(i in 1:n){ run <- sample(c(0:9),10000, replace=TRUE) cnt ...
444 sym R (407 sym/6 pcs) 1 img
data-605-week8-Assignment
data-605-week8-Assignment Ashish Kumar 03/18/2020 ==> Problem 11 on page 303 of probability text. A company buys 100 lightbulbs, each of which has an exponential lifetime of 1000 hours. What is the expected time for the first of these bulbs to burn out? According to formula \[E(v) = E_0 e ^ {-\lambda v} \] \[\lambda = \frac{1}{1000}\] \[\ n.\la...
2120 sym R (533 sym/9 pcs)
data-605-week8-Discussion
data-605-week8-Discussion Ashish Kumar 02/24/2020 Chapter SUMS OF DISCRETE RANDOM VARIABLES Exercise 1 Page 289 A die is rolled three times. Find the probability that the sum of the outcomes is:- greater than 9. Solution We know a dice has 6 sides. That means the number of possibilities per roll is 6. If we roll the dice 3 times. The total num...
731 sym R (477 sym/2 pcs)
data-605-week7-Discussion
data-605-week7-Discussion Ashish Kumar 02/24/2020 Chapter DISTRIBUTIONS AND DENSITIES Exercise 15 Page 199 Write a program for the user to input n, p, j and have the program print out the exact value of b(n, p, k) and the Poisson approximation to this value. Solution Binomial probabilities are represented as \[ f(j,n,p) = Pr(j;n,p) = Pr(X = j) =...
649 sym R (1083 sym/7 pcs)
data-605-week6-Assignment
data-605-week6-Assignment Ashish Kumar 03/04/2020 1. A box contains 54 red marbles, 9 white marbles, and 75 blue marbles. If a marble is randomly selected from the box, what is the probability that it is red or blue? Express your answer as a fraction or a decimal number rounded to four decimal places. #54 red marbles, 9 white marbles, and 75 blu...
4486 sym R (2572 sym/41 pcs) 1 img
data-605-week6-Discussion
data-605-week6-Discussion Ashish Kumar 03/02/2020 CHAPTER 3. COMBINATORICS Exercise 1 Page 88 Four people are to be arranged in a row to have their picture taken. In how many ways can this be done? Solution Position1 can be taken by all the four students Position2 can be taken by rest of the three students Position3 can be taken by rest of the t...
548 sym R (21 sym/2 pcs)
data-605-week5-Assignment
data-605-week5-Assignment Ashish Kumar 02/21/2020 Choose independently two numbers B and C at random from the interval [0, 1] with uniform density. Prove that B and C are proper probability distributions. Note that the point (B,C) is then chosen at random in the unit square. Lets consider a sample size of 100000 n <- 100000 B <- runif(n) C <- ru...
542 sym R (1134 sym/12 pcs) 2 img
data-605-week5-Discussion
data-605-week5-Discussion Ashish Kumar 02/24/2020 Chapter SIMULATION OF DISCRETE PROBABILITIES Exercise 4 Page 13 In raquetball, a player continues to serve as long as she is winning; a point is scored only when a player is serving and wins the volley. The first player to win 21 points wins the game. Assume that you serve first and have a probab...
524 sym R (1304 sym/7 pcs)
data-605-week4-Assignment
data-605-week4-Assignment Ashish Kumar 02/19/2020 Problem set 1 In this problem, we’ll verify using R that SVD and Eigenvalues are related as worked out in the weekly module. Given a 3 x 2 matrix A. \[ A = \begin{bmatrix} 1 & 2 & 3 \\ -1 & 0 & 4 \end{bmatrix} \] write code in R to compute \[X = AA^T\] and \[Y = A^TA\] Then, compute the eigen...
2428 sym R (2091 sym/31 pcs)
Week3-Assignment-Data605
data-605-week3-Assignment Ashish Kumar 02/10/2020 Problem set 1 What is the rank of the matrix A? \[ A = \begin{bmatrix} 1 & 2 & 3 & 4 \\ -1 & 0 & 1 & 3 \\ 0 & 1 & -2 & 1 \\ 5 & 4 & -2 & -3 \end{bmatrix} \] (A = matrix(c(1, 2, 3, 4, -1, 0, 1, 3,0, 1, -2, 1, 5, 4, -2, -3), nrow = 4, byrow = T)) ## [,1] [,2] [,3] [,4] ## [1,] 1 2 3...
4129 sym R (1990 sym/44 pcs)