Home » Basic probability » Uniform
Category Archives: Uniform
Uniform Spacing
Let \(U_1, U_2, U_3, U_4, U_5\) be independent uniform \((0,1)\) random variables. Let \(R\) be the difference between the max and the min of the random variables. Find
- \( E( R)\)
- the joint density of the min and the max of the \(U\)’s
- \(P( R>0.5)\)
[Pitman p. 355 #14]
Mean and Mode of Binomial
Consider a binomial\((10,p)\) distribution. If \(p\) is chosen uniformly at random from the interval \((0,1)\), what is the likelihood that the most likely number of the binomial distribution will be less than the mean of the binomial distribution?
