Suppose three cell phones are tested at random where D represent the defective cell phone and N represent the non-defective cell phone. Let X represents the number of defective cell phones that occur. , show the values of the random variable X .

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Given D represents defective cell phone while N represents non-defective cellphone

Suppose,

1) No defective cell phone occurs for the 3 successions; {NNN}, then, X=0

2) 1 defective and 2 non-defective cell phones occur; {DNN, NDN, NND}, then,

X = 1

3) 2 defective and 1 non-defectives occur; {DDN, DND,NDD} , then, X = 2

4) 3 defectives and no non-defective cell phone occurs; {DDD} , then, X = 3

Since these are the only possible outcomes, the only possible values of the random variable X are 0, 1, 2, 3