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URGENT help needed with statistics, probability
1)
A plane functions iff at least 2 of its 3 engines function.
P(each engine functions)=p, the engines operate independently of each other. Find the
probability that the plane functions.
A=engine 1, B=engine 2, C=engine 3.
P(plane functions)= P(AuB)+P(AuC)+P(BuC)
P(AnBnC)=p3
P(AnB)=P(AnC)=P(BnC)=p2
P(AuBuC)=P(A)+P(B)+P(C)-P(AnB)-P(AnC)-P(BnC)-P(AnBnC)=3p-3p2-p3
http://img168.imageshack.us/img168/2991/venn.jpg
But the regions they want are P(AuB)+P(AuC)+P(BuC) which is just 3(p-p2-2p3)
2)
2% of products in a factory are defective. Products are sold in packages of 100. What
proportion of cartons contain at least 'x' defective products? x=1,2,3,...,100. (use
binomial distribution)
Binomial distribution: P(X=x) = nCx px(1-p)n-x , where p is the probability of success.
P(defective)=0.02
P(not defective)=0.98
I need to get X~Bin(100,0.98)
P(X=x)= 100Cx0.98x0.02100-x
So my answer is just P(X=x)/100 ? (replacing P(X=x) with the above)
3)
A shipment of 8 items contain 3 that are defective. A person makes a random selection of 2
of these items, find the probability distribution for the number of defectives X. Find the
cumulative functions of X as well.
So P(X=x) is defined as follows:
0 for x<1
3/8 for 1<x<2
5/56 for 2<x<3 ( 2 defective is 3/8 * 2/7)
6/336 for x>3 (3 defective is 3/8 * 2/7 *1/6)
And to get the cdf I just integrate the functions (in the regions) between 'x' and -infinity?
Homework Statement
1)
A plane functions iff at least 2 of its 3 engines function.
P(each engine functions)=p, the engines operate independently of each other. Find the
probability that the plane functions.
The Attempt at a Solution
A=engine 1, B=engine 2, C=engine 3.
P(plane functions)= P(AuB)+P(AuC)+P(BuC)
P(AnBnC)=p3
P(AnB)=P(AnC)=P(BnC)=p2
P(AuBuC)=P(A)+P(B)+P(C)-P(AnB)-P(AnC)-P(BnC)-P(AnBnC)=3p-3p2-p3
http://img168.imageshack.us/img168/2991/venn.jpg
But the regions they want are P(AuB)+P(AuC)+P(BuC) which is just 3(p-p2-2p3)
Homework Statement
2)
2% of products in a factory are defective. Products are sold in packages of 100. What
proportion of cartons contain at least 'x' defective products? x=1,2,3,...,100. (use
binomial distribution)
Homework Equations
Binomial distribution: P(X=x) = nCx px(1-p)n-x , where p is the probability of success.
The Attempt at a Solution
P(defective)=0.02
P(not defective)=0.98
I need to get X~Bin(100,0.98)
P(X=x)= 100Cx0.98x0.02100-x
So my answer is just P(X=x)/100 ? (replacing P(X=x) with the above)
Homework Statement
3)
A shipment of 8 items contain 3 that are defective. A person makes a random selection of 2
of these items, find the probability distribution for the number of defectives X. Find the
cumulative functions of X as well.
The Attempt at a Solution
So P(X=x) is defined as follows:
0 for x<1
3/8 for 1<x<2
5/56 for 2<x<3 ( 2 defective is 3/8 * 2/7)
6/336 for x>3 (3 defective is 3/8 * 2/7 *1/6)
And to get the cdf I just integrate the functions (in the regions) between 'x' and -infinity?
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