The Binomial Distribution If a discrete random variable X has the following probability density function ( p .d.f.), it is said to have a binomial distribution : P ( X = x ) = n C x q (n- x) p x , where q = 1 - p p can be considered as the probability of a success, and q the probability of a failure. Note: n C r (“n choose r”) is more commonly written Apologies for the simple question. In several sources I found these defitions: 1) P ( X ) represents the probability of X . 2) P ( X = x ) refers to the probability that the random variable X is equal to a So, this is my first contact with Quantum Mechanics and I'm having trouble with this exercise. One of the steps involves calculating $[ X,P ]$, and I stuck there. Can anyone give me some help? Solution The possible values that X can take are 0, 1, and 2. Each of these numbers corresponds to an event in the sample space S = {h h, h t, t h, t t} of equally likely outcomes for this experiment: X = 0 to {t t}, X = 1 to {h t, t h}, and X = 2 to h h . The probability of each of these events, hence of the corresponding value of X , can be found simply by counting, to give x 0 1 2 P ( x ) 0.25 0.50 0.25 This table is the probability ...
