A fair coin is tossed 6 times. Let x = number of heads obtained. Find the value of K for which Pr(x=K+1)-Pr(x=K) is the maximum possible.
There are only 7 possible outcomes, you can do this by exhaustion. Note in this case that or for a general binomial distributed RV, .
You probably know this, but just in case . This should also be enough to get you through the other problems you posted, just write out the for each K, and do the problems by exhaustion.