To find the expected value of the distribution, we multiply each outcome by it's probability. Doing this, we get that the expected value of defects on a skateboard is of [tex]\frac{4}{25}[/tex].
Outcomes and probabilities:
0 defects, 9/10 probability
1 defect, 1/20 probability
2 defects, 1/25 probability
3 defects, 1/100 probability.
Expected value:
[tex]E(X) = 0\frac{9}{10} + \frac{1}{20} + 2\frac{1}{25} + 3\frac{1}{100} = \frac{1}{20} + \frac{2}{25} + \frac{3}{100} = \frac{5 + 8 + 3}{100} = \frac{16}{100}[/tex]
Dividing both numerator and denominator by 4:
[tex]\frac{4}{25}[/tex]
Thus, the expected value of defects on a skateboard is of [tex]\frac{4}{25}[/tex].
A similar problem is given at: https://brainly.com/question/23156292.
