Grand Canyon – Sym 506 Weekly Discussion
Describe the term mutually exclusive. Provide some examples. Must the values of x in a discrete probability distribution always be mutually exclusive? Why or why not? Provide an example.
Mutually exclusive refers to as a statistical term employed to define a situation in which one event occurrence is not caused or influenced by another event. However, it is probable for different mutually exclusive events to take place at the same time. For instance, documenting two separate roles of a single die are events which are mutually exclusive. Whichever number the dice shows on its initial roll will contain no effect on the number demonstrated in the second roll. Moreover, it is not possible for the initial and the second dice roll to take place at the same time. Discrete variables act as a good example of mutually exclusive variables. They are both mutually exclusive, meaning they cannot occur together in one event and thus variable cannot take on over one value simultaneously. Discrete variables are also exhaustive since it cannot take a value which is not the element of the variable in question. Thus, the value of x must be mutually exclusive since a discrete variable cannot have two values at the same time. It can only be one and it is only counted exclusively at an event. A good examples is days of the week. The values for the variable days of the week are discrete and mutually exclusive if x is Monday, x cannot be Tuesday at the same time. Two discrete events can only take place together if they are not related. For instance today can be Tuesday and sunny. A coin can be tossed to result to a tail, a tail and a head cannot appear together, however when a coin is tossed and a dice rolled, there is a possibility of getting a tail and a 4 from the coin and the dice respectively. Thus, when two events are not related non-mutual exclusive condition occurs but when they are related the result can only be mutually exclusive. Thus when evaluating the values for one discrete variables only one event outcome can take place at a time.