You play a game where the result could be anything from losi

You play a game where the result could be anything from losing $100 to winning $100. The game is completely random and all possibilities between losing $100 and winning $100 are equally likely.

Draw the probability density function of the amount that you win (or lose) on one play of the game.

Solution

By the given data p=1/2,q=1/2 & n=1. So P(X=x)=(ncx)*((1/2)^x)*((1/2)^(n-x))=(1cx)*(1/2). Therefore, the probability density function of the amount that you win (or lose) on one play of the game is d/dx[summation over x=0 to 1(1cx)*(1/2)]=d/dx[1(1/2)+1(1/2)]=d/dx(1)=0.