Prueba Estadistica Matematica

Distribucion binomial

x<-seq(0,10,1)
pdf_binom<-dbinom(x, 10, 0.3)
#pdf_binom
tabla<-data.frame(x, pdf_binom)
names(tabla) <-c("Var", "P(x)")
tabla

Grafica de PDF

barplot(pdf_binom, main="Binomial", xlab="Var", ylab="P(Var)", col="red", ylim=c(0, 0.3))

cdf_binom<-pbinom(x, 10, 0.3)
cdf_binom

 [1] 0.02824752 0.14930835 0.38278279 0.64961072 0.84973167 0.95265101 0.98940792 0.99840961
 [9] 0.99985631 0.99999410 1.00000000

cdf_table<-data.frame(x, cdf_binom)
names(cdf_table)<-c("var", "ac")
cdf_table

plot(x, cdf_binom, main='acumulada', xlab='var', ylab='prob', lwd='3', col='red', type='b')

Distribucion normal

y<-seq(10, 90, 0.1)
normal<-dnorm(y, mean(y),  9)
plot(y, normal, main="Distr. Normal", xlab="Variable", ylab="Densidad", lwd="2", type='l')

Calculo de probabilidad (Func)

cdf_normal<-function(z1, z2) {
  a1<-pnorm(z1, mean(y), 9)
  a2<-pnorm(z2, mean(y), 9)
  a2-a1
}
cdf_normal(40, 60)

[1] 0.7334795

\(P(40 \leq x \leq 60)=\) 0.7334795