Publications by Abdelmalek Hajjam
Data605-Assignment10
Smith is in jail and has 1 dollar; he can get out on bail if he has 8 dollars. A guard agrees to make a series of bets with him. If Smith bets A dollars, he wins A dollars with probability .4 and loses A dollars with probability .6. Find the probability that he wins 8 dollars before losing all of his money if: (a) he bets 1 dollar each time (tim...
1191 sym R (124 sym/4 pcs)
Data605-Discussion9
Exercise 10 page 339 10. Find the probability that among 10,000 random digits the digit 3 appears not more than 931 times. Answer: n <- 10000 p <- 0.1 x <- 931 pbinom(x,n,p) ## [1] 0.01064763 The probability is 0.01064763 ...
170 sym R (62 sym/2 pcs)
Data605-Assignment8
Chapter 7 Page 313 - Exercise 11 11 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? Answer: We have \(E[X_{i}]= 1/\lambda_{i}\). Therefore \(\lambda_{i}=1/1000\) . \(min X_{i} ∼ Exp(\lambda)\) where \(\lambda\) = \(\sum_{i=1}^{100} \lamb...
3912 sym R (50 sym/1 pcs)
Data605-Discussion8
Chapter 7 Page 313 - Exercise 11 11 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? Let \(X_{1}, X_{2},...,X_{100}\) be 100 lightbulbs with exponential lifetime \(\mu=1000\). The first lightbulb will burn out at minimum value of \(X_{j}\)....
2233 sym R (51 sym/2 pcs)
Data605-Assignment7
Question 1. Let X1, X2, . . . , Xn be n mutually independent random variables, each of which is uniformly distributed on the integers from 1 to k. Let Y denote the minimum of the Xi’s. Find the distribution of Y. For 1≤j≤k, \(P(Y=y) = \frac{(k−y+1)^n − (k - y)^n}{k^n}\) the number of possible combinations of \(X_i\)’s is \(k^n\) (cho...
2966 sym R (631 sym/24 pcs)
Data605-Discussion7
Chapter 5 (Distributions and Densities) - Exercise 17 page: 221 a) The density function \(f_X\) for X is nothing but the derivative of the cumulative distribution function \(F(X)\) \(d/dx(F(X)) = d/dx(sin^2(\pi x/2))\) for \(0 \le x \le 1\) We know that: \(sin^2(\theta) = (1-cos(2\theta)) / 2\) so: \(d/dx(sin^2(\pi x/2)) = d/dx((1-cos(2 \pi x/2)...
836 sym 1 img
621 Question
What is the output of this code in R? data(swiss) par(mfrow=c(2,2)) fit <- lm(swiss$Fertility~.,data=swiss) plot(fit) ...
46 sym R (82 sym/1 pcs) 1 img
Data605-Assignment6
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. RedMarble <- 54 WhitewMarble <- 9 BlueMarble <- 75 p <- round((RedMarble+BlueMarble)/(WhitewM...
4848 sym R (2417 sym/31 pcs)
Data605-Discussion-6
Exercise 2 - Page 123 2. In how many ways can we choose five people from a group of ten to form a committee? The order we choose people here does not matter. Therefore we have a combination, as long as there are 5 people choosen to form a committee. \({10\choose 5} = \frac{10!}{5!(10-5)!} = \frac{10!}{5!5!}\) so \({10\choose 5} = \frac{10*9*8*7*...
535 sym R (176 sym/2 pcs)
Data605-Assignment5
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. set.seed(101) n <- 1000000 # Create two series of random variables B and C B <- runif(n, min = 0, max = 1) C <- run...
950 sym R (1712 sym/39 pcs) 3 img