Function definition syntax confuse in Typescript

Question

I figure that out: One post in SO explain this: In TypeScript how do I declare an array of functions that accept a string and return a string?
it turns out:

A function type literal of the form

( ParamList ) => ReturnType

is exactly equivalent to the object type literal

{ ( ParamList ) : ReturnType }

So, Colon: with Bracket{} <=> Arrow =>

---

I am pretty new to Typescript, there is one example confuses me with its syntax:

var sayHello: (input: string) : string = function (s: string) {
    return "Hello " + s;
}
var stringUtils: { (input: string): string; }[];
stringUtils.push(sayHello);

Could anyone help to give a little explanation what this code do? Especially what the first part definition does?

var sayHello: (input: string) : string = function (s: string) {
    return "Hello " + s;
}

The example says sayHello is a function variable, but when I run it, I got "=>" expected error, does this mean this syntax belong to old typescript but not exist now?