Thank you for your comment, but I think the distribution for the first child should be between [1,N]. I was thinking to go ahead with the following argument:
n1 is the number of objects taken by the first child and it is uniformly distributed in [1, N], but n2 is uniformly distributed in [1...
A teacher leaves out a box of N stickers for children to take home as treats. Children form a queue and look at the box one by one. When a child finds k⩾1 stickers in the box, he or she takes a random number of stickers that is uniformly distributed on {1,2,…,k}.
1- What is the expectation of...
Thanks guys for the replies.
shreyakmath - your argument is not valid as 0- is not defined.
DonAntonio - it is a good way to proceed, but I've come to a simpler solution (may not be 100 correct).
Here is the solution:
We can show that f(x) is continious at x=1/√2 using the ε-δ...
if f : (0, 1]--> R is given by f(x) = 0 if x is irrational, and f(x) = 1/(m+n) if x = m/n in (0, 1] in lowest terms for integers m and n. How can i prove that this function is continuous at 1/√2?