Publications by Leo Yi & Christopher Bloome
605 HW 5
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. Find the probability that B + C < 1/2 P( B + C < 1/2 ) P(0 <= B <= 1/2) * P(0 <= C <= 1/2) * P(B.or.C < 1/2 - C.or.B) ...
772 sym R (627 sym/13 pcs)
605D4
Exercise ILTC27 Let T: C^3 -> C^3 be given by T(c(X,Y,Z)) = 2x + y + z x - y + 2z x + 2y - z Find K(T) Solution if T(c(X,Y,Z)) = 2x + y + z x - y + 2z x + 2y - z = 0 Then, 2x+y+z = 0 x-y+2z = 0 x+2y-z = 0 library(Matrix) library(pracma) ## Warning: package 'pracma' was built under R version 3.6.3 ## ## Attaching package: 'pracma' ## The...
269 sym R (382 sym/6 pcs)
605HW3
library(Matrix) library(pracma) ## Warning: package 'pracma' was built under R version 3.6.3 ## ## Attaching package: 'pracma' ## The following objects are masked from 'package:Matrix': ## ## expm, lu, tril, triu A <- matrix(c(1,2,3,4,-1,0,1,3,0,1,-2,1,5,4,-2,-3), nrow=4, byrow=TRUE) A ## [,1] [,2] [,3] [,4] ## [1,] 1 2 ...
818 sym R (1182 sym/22 pcs)
605 HW 7
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 . We know there are N total observations, that there are k unique values for each of these observations and that Y is the minimum. (k-Y+1)^n repre...
2975 sym R (272 sym/22 pcs)
Document605HW15
Find the equation of the regression line for the given points. Round any final values to the nearest hundredth, if necessary. x <- c(5.6, 6.3, 7, 7.7, 8.4) y <- c(8.8, 12.4, 14.8, 18.2, 20.8) df <- data.frame(x,y) df_lm <- lm(data = df , y~x) summary(df_lm) ## ## Call: ## lm(formula = y ~ x, data = df) ## ## Residuals: ## 1 2 ...
1799 sym R (806 sym/4 pcs)
Document605HW13
1 Solve the Integral below: \[ \int 4e^{-7x}dx \] \[ \frac{4}{-7} e^{-7x} + C \] 2 Biologists are treating a pond contaminated with bacteria. Find a function N( t ) to estimate the level of contamination if the level after 1 day was 6530 bacteria per cubic centimeter. $$ =-220 \ dN = (-220)dt \ N = dt-220dt \ N(1) = N_0 - - 220(1) \ N_0 = ...
1194 sym R (233 sym/4 pcs)
Document605HW12
library(RCurl) library(ggplot2) library(dplyr) ## ## Attaching package: 'dplyr' ## The following objects are masked from 'package:stats': ## ## filter, lag ## The following objects are masked from 'package:base': ## ## intersect, setdiff, setequal, union The attached who.csv dataset contains real-world data from 2008. The variab...
3505 sym R (4123 sym/20 pcs) 2 img
Document
Discussion 11 For this discussion I wanted to take a first pass at a challenge I have been meaning to attempt: the intro Kaggle challenge on Titanic survivor ship. This training data set is effectively a ship manifest for the Titanic, with an added field indicating whether they survived the iceberg or not. I converted some of the fields to “dum...
3611 sym R (9139 sym/21 pcs) 4 img
Document605HW11
Using the “cars” dataset in R, build a linear model for stopping distance as a function of speed and replicate the analysis of your textbook chapter 3 (visualization, quality evaluation of the model, and residual analysis.) The cars data set compares notes the relationship between one independent variable (Speed), and one dependent variable (...
1602 sym R (1524 sym/13 pcs) 5 img
Document605HW10
Jail Gamble Game 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 dolla...
1038 sym R (85 sym/4 pcs)