I'm studying probabilities and I came across the following problem
The problem is:
Anew digital scale accuracy may be acceptable (A) or unacceptable (U). A certain lab experiment required 2 scales will be independently selected and tested until 2 acceptable scales have been found. Suppose 80% of the new scales have an acceptable degree of accuracy. Let Y denote the number of scales that must be tested.
a. what is the random variable in the above question?
b. what is p(y=2)
c. what is p(3)? note there are 2 different outcomes the result Y=3
d. In order to have Y=5, what must be true of the 5th scale selected?
e. list the four outcomes for which Y=5 and then calculate p(5)?
My answers.
This question seems -ve binomial distribution.
so,
a- the random variable is Y
b- using this formula b(x; n, P) = nCx * Px * (1 - P)n - x, we can find p(2)..etc
so we have
n=2
p=.8
q=.2
p(2)=.64
p(3)=.204
but I couldn't figure out how I can find the outcomes!! what does it mean to have two different outcomes that result Y=3
if we find the sample space out come it will be like this {AA,UA,AU,UU}
Can anybody help!!!:roll:
Many thanks:-D
The problem is:
Anew digital scale accuracy may be acceptable (A) or unacceptable (U). A certain lab experiment required 2 scales will be independently selected and tested until 2 acceptable scales have been found. Suppose 80% of the new scales have an acceptable degree of accuracy. Let Y denote the number of scales that must be tested.
a. what is the random variable in the above question?
b. what is p(y=2)
c. what is p(3)? note there are 2 different outcomes the result Y=3
d. In order to have Y=5, what must be true of the 5th scale selected?
e. list the four outcomes for which Y=5 and then calculate p(5)?
My answers.
This question seems -ve binomial distribution.
so,
a- the random variable is Y
b- using this formula b(x; n, P) = nCx * Px * (1 - P)n - x, we can find p(2)..etc
so we have
n=2
p=.8
q=.2
p(2)=.64
p(3)=.204
but I couldn't figure out how I can find the outcomes!! what does it mean to have two different outcomes that result Y=3
if we find the sample space out come it will be like this {AA,UA,AU,UU}
Can anybody help!!!:roll:
Many thanks:-D