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• Notes

Four electronic ovens that were dropped during ship-
ment are inspected and classified as containing either a major,
a minor, or no defect. In the past, $60\%$ of dropped ovens had
a major defect, $30\%$ had a minor defect, and $10\%$ had no
defect. Assume that the defects on the four ovens occur
independently.

(a) Is the probability distribution of the count of ovens in each
category multinomial? Why or why not?
(b) What is the probability that, of the four dropped ovens, two
have a major defect and two have a minor defect?
(c) What is the probability that no oven has a defect?
Id) The expected number of ovens with a major defect.
(e) The expected number of ovens with a minor defect.

4 elec oven
- Major defect $60\%$ x
- minor defect $30\%$ y
- no defect $10\%$ z

(a) - trials are independent

- Major defect, minor, no defect

$\rightarrow$ multinomial distribution

(b) $P\left(x=2, y=2, z=0\right)$

$=\frac{4 !}{2 ! 2 ! 0 !} \times 0.6^{2} \times 0.3^{2} \times 0.1^{0}$

$=0.1944$

(c) $P(x=0, y=0, z=4)$

$=\frac{4 !}{0 ! 0 ! 4 !} \times 0.6^{0} \times 0.3^{0} \times 0.1^{4}$

$=0.0001$

(d) $E(x)=n P_{x}$

$=4 \times 0.6=2.4$

(e) $E(y)=n P_{y}$

$=4 \times 0.3=1.2$