Answer to Question #174853 in Statistics and Probability for Cyrille

Question

Suppose three laptops are tested.Let D represent the defective laptop and N for the non defective laptops.how many possible outcomes will occur from the experiment and what are the possible values of the random variable?

Answer 1

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

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

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

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

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

4) In case 4 all three cellphones are defective. 𝑋 has a 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 ∈ {0,1,2,3}.