# Find expectation of a probablity distribution [duplicate]

There're k balls in a bag, each one with a different colour. Draw one ball from the bag randomly each time, then put the ball back.

Let random variable X = the number of balls to draw until all k colours have been seen. Find E(X).

## marked as duplicate by joriki probability StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Jun 18 '16 at 1:07
This is the "coupon collector's problem". As the Wikipdia article explains, the expected value is $k$ times the $k$th harmonic number: $$k\left( 1 + \frac 1 2 + \frac 1 3 + \cdots + \frac 1 k \right).$$