Publications by Laura Burenkov
Story 5
Historic data indicates that the occurrence and intensity of cyclonic storms (Hurricanes, Typhoons and Tornados) increases with the increased earth temperature. For this assignment you will need to tell this story to a non-technical audience (eg: a high-school earth science class). Notes: Source historic data for a period of at least 25 years on...
14277 sym Python (24639 sym/44 pcs) 9 img
Homework 10
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 he bets 1 dollar each time (timid ...
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Discussion 10
Exercise 7 Show that the probability of no equalization in a walk of length 2m equals u2 To show that the probability of no equalization in a walk of length \(2m\) equals \(u^2\), where \(u\) is as defined earlier, we need to understand the concept of equalization in a walk. In a random walk of length \(2m\), an equalization occurs when the num...
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Discussion 9
Exercise 4 Let S be the number of heads in 1,000,000 tosses of a fair coin. Use (a) Chebyshev’s inequality, and (b) the Central Limit Theorem, to estimate the probability that S lies between 499,500 and 500,500. Use the same two methods to estimate the probability that S lies between 499,000 and 501,000, and the probability that S lies betwee...
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Data 605 A8
Exercise 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? To solve this problem, we can use the concept of exponential distribution and the memorylessness property of exponential random variables. Let \(X_i\) be the lifetime of the \(i...
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Discussion 8
Exercise 9 Assume that the service time for a customer at a bank is exponentially distributed with mean service time 2 minutes. Let X be the total service time for 10 customers. Estimate the probability that X > 22 minutes. #Step 1: Defining Parameters rate <- 1/2 # rate parameter (λ) of the exponential distribution #Step 2: Calculating Gam...
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Data 607 week 7
library(tidyverse) library(openintro) Exercise 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 . # Define a function to calculate the PMF of Y pmf_Y <- function(y, k, n) { prob_Y_ge_y <-...
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Discussion 7
Exercise 10 Let U, V be random numbers chosen independently from the interval [0, 1]. Find the cumulative distribution and density for the random variables (a) Y = max(U, V ). (b) Y = min(U, V ). #Setting the seed for reproducibility set.seed(123) #Simulating random variables U and V U <- runif(1000, 0, 1) # Generate 1000 random numbers from...
2018 sym Python (1004 sym/2 pcs) 1 img
Story 3
library(tidyverse) library(openintro) library(httr) library(jsonlite) library(plotly) ## Warning: package 'plotly' was built under R version 4.3.3 Instructions The CDC publishes firearm mortality for each State per 100,000 persons https://www.cdc.gov/nchs/pressroom/sosmap/firearm_mortality/firearm.htm. Each State’ firearm control laws can ...
11622 sym R (24055 sym/11 pcs)
Data 605 A6
library(tidyverse) library(openintro) Exercise 1 A bag contains 5 green and 7 red jellybeans. How many ways can 5 jellybeans be withdrawn from the bag so that the number of green ones withdrawn will be less than 2? # Number of green jellybeans num_green <- 5 # Number of red jellybeans num_red <- 7 # Total number of jellybeans to be withdr...
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