MVVM: Binding to ListBox.SelectedItem isn't being updated?

How do I bind a view model property to the ListBox.SelectedItem property?

I have created a simple MVVM demo to try to figure this one out. My view model has these properties:

private ObservableCollection<DisneyCharacter> p_DisneyCharacters;
public ObservableCollection<DisneyCharacter> DisneyCharacters
{
    get { return p_DisneyCharacters; }

    set
    {
        p_DisneyCharacters = value;
        base.FirePropertyChangedEvent("DisneyCharacters");
    }
}

private DisneyCharacter p_SelectedItem;
public DisneyCharacter SelectedItem
{
    get { return p_SelectedItem; }

    set
    {
        p_SelectedItem = value;
        base.FirePropertyChangedEvent("SelectedItem");
    }
}

I want to bind the SelectedItem property to the item selected in the list box. Here is the XAML for the list box:

<ListBox ItemTemplate="{StaticResource MasterTemplate}"
         ItemsSource="{Binding Path=DisneyCharacters}" 
         SelectedItem="{Binding Path=Selectedtem, Mode=TwoWay}" 
         HorizontalAlignment="Stretch" />

Here is my problem: The view model SelectedItem property isn't being updated when I change the selection in the list box.

I did a test where I temporarily replaced the view model SelectedItem property with a SelectedIndex property, and I bound that to the ListBox.SelectedIndex property. That property updated fine--it's just the SelectedItem property that I can't get to work.

So, how do I fix the SelectedItem binding? Thanks for your help.