# how to scale the plot of PDF (t-distribution)

The directions in my book say: "To sketch the t distribution in Figure 3.11, simply multiply the abscissa t value by the scale factor and plot this against the ordinate of t at that point." So basically, the scale factor is given. The x values should be multiplied by the scaled factor while the y should remain the same. It seems like all it is, we are stretching the plot of t distribution by the scale factor. How do I create a plot like this? For a normal t-distribution, I would use the following code for plotting. But how do I produce a plot as described above?

Plot[PDF[StudentTDistribution, x], {x, -8, 8 }]


Edit: I just realized that I also need to scale the whole graph by the scale parameter: i.e. the shape remains the same, but I need to operate on much larger values of x

• Plot[PDF[StudentTDistribution, x/scalefactor], {x, -8, 8}]? – Algohi Feb 8 '15 at 0:53
• @Algohi, thanks! what if I wanted to change the scale for x and y? in other words, to see exactly the same plot (shape) of data, but on bigger scale? – dark blue Feb 8 '15 at 1:17

I am not sure if I understand you correctly but you can try this:

f[sclx_, scly_] := scly*PDF[StudentTDistribution, x/sclx]
Plot[{f[1, 1], f[2, 3]}, {x, -8, 8}] • How can both of these curves be a valid pdf? – wolfies Feb 8 '15 at 14:07
• Only one is valid pdf. – Algohi Feb 8 '15 at 16:56
• What is the other? – wolfies Feb 8 '15 at 18:04
• The other is a function resulted from the first one. – Algohi Feb 8 '15 at 18:17
• \\\\\ . :-) . //// – wolfies Feb 9 '15 at 3:00