R Notebook

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1. Code to compute with our probabilities pi contained in the vector p

exactlyone <- function(p) {
notp <- 1 - p
tot <- 0.0
for (i in 1:length(p))
tot <- tot + p[i] * prod(notp[-i])
return(tot)
}

2. the functions to return cumulative sums and product

x <- c(25,55,133)
cumsum(x) #to return cumulative sums

## [1]  25  80 213

cumprod(x) #to return cumulative products

## [1]     25   1375 182875

3. Minima & Maxima

nlm(function(x) return(x^2-sin(x)),8)

## $minimum
## [1] -0.2324656
## 
## $estimate
## [1] 0.4501831
## 
## $gradient
## [1] 4.024558e-09
## 
## $code
## [1] 1
## 
## $iterations
## [1] 5

4. Minima & Maxima

nlm(function(x) return(3*2-cos(x)),8)

## $minimum
## [1] 5
## 
## $estimate
## [1] 6.283182
## 
## $gradient
## [1] -1.176099e-07
## 
## $code
## [1] 1
## 
## $iterations
## [1] 4

5. Calculus

D(expression(exp(x^2)),"x") # derivative

## exp(x^2) * (2 * x)

6. Calculus

D(expression(exp(x^3)+x),"x") # derivative

## exp(x^3) * (3 * x^2) + 1

7. Integrate exp(x^2) between 0 and 1

integrate(function(x) x^2,0,1)

## 0.3333333 with absolute error < 3.7e-15

8. Set Operations

x1 <- c(2,20,200)
y1 <- c(50,200,2,90)

8.1. combine unique values

union(x1,y1)

## [1]   2  20 200  50  90

8.2. select which intersect in both x1 & y1

intersect(x1,y1)

## [1]   2 200

8.3. select which of x1 not part of y1

setdiff(x1,y1)

## [1] 20

8.4. select which of y1 not part of x1

setdiff(y1,x1)

## [1] 50 90