Question

Suppose three cell phones are tested randomly. We want to find out the number of defective cellphones that occur.
Let D represent the defective and N for non-defective cell phone. If we let X be the random variable representing the number of cell phones, can you show the values of random variable X?

Answer 1

Answer on Question #63600 – Math – Statistics and Probability

Question

Suppose three cell phones are tested randomly. We want to find out the number of defective cellphones that occur.

Let D represent the defective and N for non-defective cell phone. If we let X be the random variable representing the number of cell phones, can you show the values of random variable X?

Solution

We want to find out the number of defective cellphones that occur in test.

After testing of the cell phones we can receive 4 types of result:

1) In the case 1 all cell phones are working. So we have 0 cell phones that don't work and X has value 0.

2) In the case 2 only one of the phones is broken and others are good. Then X has value 1.

3) In the case 3 we have two broken cellphones and one working cellphone. So X has value 2.

4) In the case 4 all three cellphones are defective. X has value 3.

After analysis of all possible cases we receive that X may be equal to 0, 1, 2 or 3.

Distribution law for X:

Here $p_i$ stands for probability of the $i$-th case and

$$\sum_{i=0}^{3} p_i = 1.$$

Answer: $X \in \{0,1,2,3\}$.

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