For the first one, can you show that the median occurs at that point? If your distribution is symmetric, can you show the mean occurs at that point? (Hint: your distribution has 1/2 for a 0 value and 1/2 for a 1 value for every X_k).
Hoi, i dont see why the following is true
Let ( i.i.d. Bernoulli trials)
and consider ( Then clearly )
Apparantly the distribution function F of Y is constant on the interval and satisfies
and
for it satisfies
I'm a bit bewildered...:/
For the first one, can you show that the median occurs at that point? If your distribution is symmetric, can you show the mean occurs at that point? (Hint: your distribution has 1/2 for a 0 value and 1/2 for a 1 value for every X_k).