Publications by Devin Teran
Week6Discussion
Page 113 Exercise 2 Using R: In how many ways can we choose five people from a group of ten to form a committe n <- 10 k <- 5 choose(n,k) ## [1] 252 By Hand: \[{10 \choose 5}\] \[{10! / (5!*(10-5)!)}\] \[{10! / (5!*5!)}\] \[{(10*9*8*7*6) / (5*4*3*2)}\] \[{30240 / 120}\] \[{252}\] ...
252 sym R (37 sym/2 pcs)
Week7Homework
Problem 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. This problem was very difficult and I used resources to come up with solution seen in references below. Definitely a challening problem...
1793 sym R (1960 sym/16 pcs)
Week8
Problem 11 - Page 303 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? (See Exercise 10.) The expected time for the first of these bulbs to burn out is 10 hours. λ = 1/1000 Expected_value = 1 / (100*λ) Expected_value ## [1] 10 Problem 14...
1299 sym R (536 sym/10 pcs)
Week9Discussion
Exercise 1 Let S100 be the number of heads that turn up in 100 tosses of a fair coin. Use the Central Limit Theorem to estimate (a) P(S100 ≤ 45). n = 100 p = 0.5 q = 1-p sd = sqrt(n*p*q) expected = n*p value = (45.5 - expected) / sd pnorm(value) ## [1] 0.1840601 P(45 < S100 < 55). n = 100 p = 0.5 q = 1-p sd = sqrt(n*p*q) expected = n*p valu...
206 sym R (539 sym/8 pcs)
Week9Assignment
Problem 11 - Page 363 The price of one share of stock in the Pilsdorff Beer Company (see Exercise 8.2.12) is given by Yn on the nth day of the year. Finn observes that the differences Xn = Yn+1 − Yn appear to be independent random variables with a common distribution having mean µ = 0 and variance σ2 = 1/4. If Y1 = 100, estimate the probabili...
2999 sym R (247 sym/6 pcs)
Final_DTeran
Final Exam Problem 1 a P(X>x | X>y) b P(X>x, Y>y) c (X<x | X>y) Investigate whether P(X>x and Y>y)=P(X>x)P(Y>y) by building a table and evaluating the marginal and joint probabilities. Check to see if independence holds by using Fisher’s Exact Test and the Chi Square Test. What is the difference between the two? Which is most appropriate? Pro...
9294 sym R (47795 sym/81 pcs) 8 img
Week14Assignment
Taylor Series Expansions This week, we’ll work out some Taylor Series expansions of popular functions. The function for Taylor series is: \[f(x) = \sum_{n=0}^{\infty}\frac{f^{(n)}(0)}{n!}x^{n}\] Here are the functions we’ll be working through: \[f(x) = \frac{1}{(1−x)}\] \[f(x) = e^{x}\] \[f(x) = ln(1 + x)\] For each function, only consider ...
2891 sym
DTeran_Week13Assignment
1. Use integration by substitution to solve the integral below. \[\int 4 e^{-7x}~dx\] This is the same as: \[-4/7\int -7 e^{-7x}~dx\] If u = -7x, \[\frac{du}{dx} = -7 \] \[du = -7 dx \] And rearranging the problem we get: \[-4/7\int -7~dx e^{-7x}\] Which is the same as: \[-4/7\int du e^{u}\] And the integral of e^u is e^u so we can solve for the ...
3067 sym R (392 sym/5 pcs) 1 img
Week12Assignment
Load & View the Data Country: name of the country LifeExp: average life expectancy for the country in years InfantSurvival: proportion of those surviving to one year or more Under5Survival: proportion of those surviving to five years or more TBFree: proportion of the population without TB. PropMD: proportion of the population who are MDs PropRN: ...
5315 sym R (4179 sym/18 pcs) 2 img
Week11 Assignment
Using R’s built in car data we are going to build a linear model to try and predict distance using car speed. First let’s view the data we’re working with: head(cars) ## speed dist ## 1 4 2 ## 2 4 10 ## 3 7 4 ## 4 7 22 ## 5 8 16 ## 6 9 10 Let’s see if there might be a linear relationship between the...
2184 sym R (1213 sym/11 pcs) 5 img