R Markdown

1.

factorial(8)/ (factorial(2) * factorial(3))

## [1] 3360

factorial(9)

## [1] 362880

library(MASS)
choose(16,2)/choose(20,2)

## [1] 0.6315789

Part B #1.

#dbinom(x,n,p)
sum(dbinom(7:10,10,.5))

## [1] 0.171875

#dbinom(x,n,p)
sum(dbinom(3:5,5,.6))

## [1] 0.68256

#dbinom(x,n,p)
sum(dbinom(5:6,6,.75))

## [1] 0.5339355

1-sum(dbinom(5:6,6,.75))

## [1] 0.4660645

Part C #1.

pnorm(20,25,5.25)

## [1] 0.1704519

y <- c(-100:100) 
z<- dnorm(y, mean=25, sd=5.25)
plot(z)

plot(y)

plot(y,z)

x <- c(-3,6,9)
p <- c(1/6, 1/2, 1/3)

#A. # E(x)
expectation <- sum(x*p)
expectation

## [1] 5.5

(x%*%p)

##      [,1]
## [1,]  5.5

 # E[g(x)]= sum(g(x)*p)
#B. # E(x^2)
sum(x^2 * p)

## [1] 46.5

#C.E((2x+1)^2) 
sum((2*x*p)+1)^2

## [1] 196

#4 Part D E[(x-u)^2]
# where u= E(x)
sum((x-5.5)^2)

## [1] 84.75

((x-5.5)^2)

## [1] 72.25  0.25 12.25

#E(x)= expectation

#Part E sigma(x)= sqrt(v(x))
sqrt(sum((x-5.5)^2))

## [1] 9.205976

#Part F
#V(2x+1)
sum((2*(x-5.5)+1^2))

## [1] -6

#dpois(x,"landa")
dpois(5,4)

## [1] 0.1562935

#B. P(x<5)
sum(dpois(0:4, 4))

## [1] 0.6288369

#C. P(X>=5)
1-(sum(dpois(0:4, 4)))

## [1] 0.3711631