How would I do global chat message deaths?

Forgive me if I'm an idiot, and my code is messy.

I tried using a LocalScript inside of StarterCharacterScripts that uses math.random(1,3) to choose a death message, which worked, but I wasn't satisfied with it, as the death messages are local.

How would I go about doing global randomized death messages? I was thinking of using a RemoteEvent for a server-sided Script. Would that work? Is there a much simpler option that I'm not seeing?

LocalScript inside of StarterCharacterScripts:

game.Players.LocalPlayer.Character.Humanoid.Died:Connect(function()
	local mr = math.random(1,3)
	local red = BrickColor.new('Bright red')
	local deadPlayer = game.Players.LocalPlayer.Character.Name
	
	if mr == 1 then
		game.StarterGui:SetCore("ChatMakeSystemMessage", {
			Text = deadPlayer.. " tripped!";
			Font = Enum.Font.Highway;
			Color = red.Color;
			FontSize = Enum.FontSize.Size96;
		})
	end
	
	if mr == 2 then
		game.StarterGui:SetCore("ChatMakeSystemMessage", {
			Text = deadPlayer.. " stepped on a landmine!";
			Font = Enum.Font.Highway;
			Color = red.Color;
			FontSize = Enum.FontSize.Size96;
		})
	end
	
	if mr == 3 then
		game.StarterGui:SetCore("ChatMakeSystemMessage", {
			Text = deadPlayer.. " found a Creeper!";
			Font = Enum.Font.Highway;
			Color = red.Color;
			FontSize = Enum.FontSize.Size96;
		})
	end
end)

Also, my main is "LukeMasterVader", if you're curious. Haven't used this site in years, so I forgot my password, and I don't even know what email I signed up with.

I would use a main script that tracks the death of each player and use FireAllClients to notify players.

Script

local Players = game:GetService("Players")
local PlayerDiedChatEvent = game:GetService('ReplicatedStorage'):WaitForChild('PlayerDiedChatEvent')

local function PlayerJoined(Player) 
	Player.CharacterAdded:Connect(function(character)
		local Humanoid = character:WaitForChild("Humanoid")
		if Humanoid then 
			Humanoid.Died:Connect(function()
				PlayerDiedChatEvent:FireAllClients(Player)
			end)
		end
	end)
end

Players.PlayerAdded:Connect(function(Player)
	PlayerJoined( Player )
end)

for _, Player in pairs(Players:GetPlayers()) do 
	PlayerJoined(Player)
end

LocalScript

local PlayerDiedChatEvent = game:GetService('ReplicatedStorage'):WaitForChild('PlayerDiedChatEvent')

PlayerDiedChatEvent.OnClientEvent:Connect(function(PlayerWhoDied)
	print (PlayerWhoDied, 'just kicked the can')
end)