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

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

To plot the probability density function, we need to specify **df **(degrees of freedom) in the **dt() **function along with the **from **and **to **values in the **curve() **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 the **legend() **function, which takes on the following syntax:

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

where:

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