1) There are n balls numbered from 1 to n in an urn. It is completely not depending purely randomly, a ball drawn with replacement. The random variable X denotes the smallest of the ball numbers...

Extracted text: 1) There are n balls numbered from 1 to n in an urn. It is completely not depending purely randomly, a ball drawn with replacement. The random variable X denotes the smallest of the ball numbers observed. Show that: a) P(X > k) = (1 –4)" , k=1,2, ...,n. b) P(X – 1= k) –→ p(1 – p)k for n → , ke NU{0}, where p= 1-e-1 They say the random variable X -1 converges in distribution to the geometric distribution with parameter p = 1 -e-