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To plot the probability density function for a t distribution in R, we can use the following functions:

**dt(x, df)**Â to create the probability density function**curve(function, from = NULL, to = NULL)**Â to plot the probability density function

To plot the probability density function, we need to specify **dfÂ **(degrees of freedom)Â in theÂ **dt()Â **function along with theÂ **fromÂ **and **toÂ **values in theÂ **curve()Â **function.

For example, the following code illustrates how to plot a probability density function for a t distribution with 10 degrees of freedom where the x-axis of the plot ranges from -4 to 4:

curve(dt(x, df=10), from=-4, to=4)

Similar to the normal distribution, the t distribution is symmetrical around a mean of 0.

We can add a title, change the y-axis label, increase the line width, and even change the line color to make the plot more aesthetically pleasing:

curve(dt(x, df=10), from=-4, to=4, main = 't Distribution (df = 10)', #add title ylab = 'Density', #change y-axis label lwd = 2, #increase line width to 2 col = 'steelblue') #change line color to steelblue

We can also add more than one curve to the graph to compare t distributions with different degrees of freedom. For example, the following code creates t distribution plots with df = 6, df = 10, and df = 30:

curve(dt(x, df=6), from=-4, to=4, col='blue') curve(dt(x, df=10), from=-4, to=4, col='red', add=TRUE) curve(dt(x, df=30), from=-4, to=4, col='green', add=TRUE)

We can add a legend to the plot by using theÂ **legend()Â **function, which takes on the following syntax:

**legend(x, y=NULL, legend, fill, col, bg, lty, cex)**

where:

**x, y:**Â the x and y coordinates used to position the legend**legend:**Â the text to go in the legend**fill:**Â fill color inside the legend**col:Â**the list of colors to be used for the lines inside the legend**bg:Â**the background color for the legend**lty:Â**line style**cex:Â**text size in the legend

In our example we will use the following syntax to create a legend:

#create density plots curve(dt(x, df=6), from=-4, to=4, col='blue') curve(dt(x, df=10), from=-4, to=4, col='red', add=TRUE) curve(dt(x, df=30), from=-4, to=4, col='green', add=TRUE) #add legend legend(-4, .3, legend=c("df=6", "df=10", "df=30"), col=c("blue", "red", "green"), lty=1, cex=1.2)