04-13-In-class exercises-1

#load data& see it  /when df=3

#
x <- seq(-pi*2, 2*pi, .05)
z <- dnorm(x)
y <- dt(x, df=3)
plot(x, z, type="l", bty="L", xlab="Standard unit", ylab="Density")
polygon(c(x, rev(x)), c(y, rev(z)), col='aliceblue')
lines(x, y, col='cadetblue')

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#when df=10

#
x <- seq(-pi*2, 2*pi, .05)
z <- dnorm(x)
y <- dt(x, df=10)
plot(x, z, type="l", bty="L", xlab="Standard unit", ylab="Density")
polygon(c(x, rev(x)), c(y, rev(z)), col='aliceblue')
lines(x, y, col='cadetblue')

###

#when df=100

#
x <- seq(-pi*2, 2*pi, .05)
z <- dnorm(x)
y <- dt(x, df=100)
plot(x, z, type="l", bty="L", xlab="Standard unit", ylab="Density")
polygon(c(x, rev(x)), c(y, rev(z)), col='aliceblue')
lines(x, y, col='cadetblue')

###
#increasing degree of freedom will approximate normal distribution