A chess player named Guy has two chess games at the upcoming weekend. Guy has a 0.6 probability of not losing the first game and 0.4 probability of not losing the second game. If Guy doesn't lose, he has a 0.5 probability of a win and a 0.5 probability of a tie, independent of any events during the weekend. Guy will receive 2 points for the win, 1 point for the tie, and 0 point for the loss.
Discrete random variable will consist of values of all the possible points Guy will end up with after playing two games.
What is a PMF value that Guy will end up with 2 points after both games had been played?
Tip:
Steps:
- Represent an experiment in terms of discrete random variable: Represent possible points at the end of two games as values in a random variable.
- Specify the Sample Space () of the experiment: All possible points at the end of two games.
- Specify the Probability Law for the experiment: Associate probabilities for each possible point.
- Associate a PMF to a discrete random variable: PMF formula.
- Calculation PMF: Apply PMF formula when the value in the random variable is 2 points.