MathDB

10. In an urn there are balls of

N

different colours,

n

balls of each colour. Balls are drawn and not replaced until one of the colours turns up twice; denote by

V_{N,n}

the number of the balls drawn and by

M_{N,n}

the expectation of the random variable

v_{N,n}

. Find the limit distribution of the random variable

\frac{V_{N,n}}{M_{N,n}}

N \to \infty

and

n

is a fixed number. (P. 8)

10