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Question by Max: Probability help?!?!?
An injection molding process leaves an average of 1.3 defects per bumper. Let Y and Z be the next two bumpers produced. Use an appropriate prob. function to evaluate:
a.)P[Y=2]
b.)P[Y>=1]
c.)sqr(Var Y)
d.)P[Y+Z>=2]

Best answer:

Answer by efqy
You’re presumably meant to assume a Poisson distribution with parameter 1.3

[The definition of Y and Z are wrong, and if your teacher/lecturer/textbook actually put that (“Let Y and Z be the next two bumpers produced”) they should be ashamed .

Y and Z should be “the number of defects on the next two bumpers produced, respectively”. If Y and Z were the bumpers themselves, they would not take values like 2, because bumpers are not numbers.]

a) just substitute 2 into the Poisson probability function with parameter 1.3

b) This is 1-P(Y=0)

c) what’s the variance of a Poisson random variable?

d) What’s the distribution of the sum of two independent Poissons?

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