*ANSWER* checking the answer of Q1
Dear all,
For Q1, I got nu_min around 0.375. Therefore, [d] would be the closet answer.
I feel the answer is reasonable, for the following consideration:
1. The probablity of getting no head outcomes in 10 trails is 1/1024.
2. For 1000 tentimesthrown coins, the probability of getting no one with head count = 0 is [(10241)/1024]^1000 = 0.375.
3. In most cases, when there is no one with head count =0, the lowest head count is most likely to be 1.
4. Therefore, the expectation value of nu_min will be approximately 0*0.625 + 1*0.375 = 0.375.
Am I doing anything wrong? Or I misunderstood the question?
