[Ezra Halleck]

A shipment of parts contains 40 items of which 5 are defective. Ten of these items are randomly chosen and inspected. Let X denote number that are defective. Let be the random variable that is 1 if the ith part selected is defective and 0 otherwise. Note that .
a) Find expressions for probability distribution of X (leave as a product and/or ratio of binomial coefficients).
b) Expand the probability for your first outcome so that it is product and/or ratio of integers.
c) Write the Excel command to find probability for your first outcome.
d) Find the distribution and expectation for .
e) Use part d) and the fact that expectation distributes over a sum regardless of independence to find E[X].
f) Expectation is a measure of a distribution’s center. In light of your calculation from e), discuss the graph of X. Is it symmetric? skewed? If so, in which direction?

[Ruslan Yelizarov]

See the attached file for solution

[This_is_Anarchy]

Professor, can you post a solution to this particular question? It’s a bit confusing, perhaps i’m missing something.

[leyla]

for b) i did (35 nCr 10)/(40nCr10) and got the .21658 you get from when you do it on excel.

[This_is_Anarchy]

Okay, I see what I was doing wrong.

[This_is_Anarchy]

Ruslan did it correctly, not sure about B though. I believe leyla is right.

[fladmer911]

that’s what I got

[ALOYSIUS ROBERTS]

Yes! keep trying.

[ALOYSIUS ROBERTS]

DATA INFORMATION