# Thread: Mathematica - Slot (#n)

1. ## Mathematica - Slot (#n)

I am trying to more easily display a plot of four functions by using slot but I am having trouble getting it to work:

Plot[PDF[FRatioDistribution[#1, #2], x] &[{1, 10}, {1, 10}], {x, 0, 3}, PlotStyle -> {Red, Green, Blue, Yellow}]

Basically, I want a plot of four F-distributions with parameters (1,1), (1,10), (10,1), (10,10)

I almost had it working with another distribution (it works except for the coloring):

Plot[(E^(-(Sqrt[(2 k)/#1] - #3)^2/(2*(#2)^2)) + E^(-(-Sqrt[((2 k)/#1)] - #3)^2/(2*(#2)^2)))/(2*#2*Sqrt[\[Pi]*#1*k]) &[1, 2, {0, 1, 2}], {k, 0, 4}, PlotRange -> {0, 0.3}, Filling -> Axis, PlotStyle -> {Red, Green, Blue}]

Oddly, if I evaluate this on separate lines the coloring works correctly:

(E^(-(Sqrt[(2 k)/#1] - #3)^2/(2*(#2)^2)) + E^(-(-Sqrt[((2 k)/#1)] - #3)^2/(2*(#2)^2)))/(2*#2*Sqrt[\[Pi]*#1*k]) &[1, 2, {0, 1, 2}]

Plot[%, {k, 0, 4}, PlotRange -> {0, 0.3}, Filling -> Axis, PlotStyle -> {Red, Green, Blue}]

Any help would be greatly appreciated.

2. ## Simpler Question

Maybe I should attack this question in stages. Does anyone know why this works as I would expect:

#1 + #2 &[1, {1, 2}]
={2, 3}

but this does not:

#1 + #2 &[{1, 2}, {1, 2}]
={2, 4}

I would like it to give {2, 3, 4}. I know this can be done with table, but I am trying to learn how to use the power of Slot. Thanks.