Homework6

R Markdown

This is an R Markdown document. Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents. For more details on using R Markdown see http://rmarkdown.rstudio.com.

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summary(cars)

##      speed           dist       
##  Min.   : 4.0   Min.   :  2.00  
##  1st Qu.:12.0   1st Qu.: 26.00  
##  Median :15.0   Median : 36.00  
##  Mean   :15.4   Mean   : 42.98  
##  3rd Qu.:19.0   3rd Qu.: 56.00  
##  Max.   :25.0   Max.   :120.00

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#2

z <- 3:5
sum(dhyper(z, 5, 10, 7))

## [1] 0.4265734

#3

lambda <- 3
p_gt_2 <- 1 - ppois(2, lambda)
c('P(X > 2) =', p_gt_2)

## [1] "P(X > 2) ="        "0.576809918873157"

sum(dbinom(x = 5:20, size = 20, prob = p_gt_2))

## [1] 0.9993216

set.seed(123)

#4

x <- 6.05
log_x <- log(x)
p <- pnorm(log_x, mean = 3, sd = sqrt(1.44))
c('P(X ≤ 6.05) =', round(p, 4))

## [1] "P(X ≤ 6.05) =" "0.1587"