4Nelly is diving for oysters. Each oyster may or may not contain a pearl. Use random variable X for the number of oysters she finds and random variable Y for the number of pearls she finds.   Their joint distribution is given in the following table:         Pearls Y           0 1 2 3 4 sum   0 0.3 0 0 0 0 0.3 Oysters X 1 0.0625 0.1875 0 0 0 0.25   2 0.0125 0.075 0.1125 0 0 0.2   3 0.0023 0.0211 0.0633 0.0633 0 0.15   4 0.0004 0.0047 0.0211 0.0422 0.0316 0.1   sum 0.3777 0.2883 0.1969 0.1055 0.0316 1   4.iFor a given dive, what is the probability that Nelly does not find any oysters that do not contain a pearl (so any oyster found will contain a pearl)? (3 decimals accuracy.)   a) 0 b) 0.3 c) 0.395 d) 0.622 e) 0.695 f) 0.7 g) Other _____   4.iiSuppose that Nelly finds at least 2 oysters. What is then the probability that she does not find any pearls? (3 decimals accuracy.)   a) 0 b) 0.015 c) 0.034 d) 0.170 e) 0.828 f) Other _____   4.iiiWhat is the correlation coefficient between the number of Oysters and the number of Pearls? (1 decimal accuracy.)   a) 999 b) 0 c) 0.1 d) 0.2 e) 0.3 f) 0.4 g) 0.5 h) 0.6 i) 0.7 j) 0.8 k) 0.9 l) 1 m) Other _____

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Chapter1: Combinatorial Analysis
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4

Nelly is diving for oysters. Each oyster may or may not contain a pearl. Use random variable X for the number of oysters she finds and random variable Y for the number of pearls she finds.

 

Their joint distribution is given in the following table:


       

Pearls Y

     
 

 

0

1

2

3

4

sum

 

0

0.3

0

0

0

0

0.3

Oysters X

1

0.0625

0.1875

0

0

0

0.25

 

2

0.0125

0.075

0.1125

0

0

0.2

 

3

0.0023

0.0211

0.0633

0.0633

0

0.15

 

4

0.0004

0.0047

0.0211

0.0422

0.0316

0.1

 

sum

0.3777

0.2883

0.1969

0.1055

0.0316

1

 

4.i

For a given dive, what is the probability that Nelly does not find any oysters that do not contain a pearl (so any oyster found will contain a pearl)? (3 decimals accuracy.)

 

a) 0

b) 0.3

c) 0.395

d) 0.622

e) 0.695

f) 0.7

g) Other _____

 

4.ii

Suppose that Nelly finds at least 2 oysters. What is then the probability that she does not find any pearls? (3 decimals accuracy.)

 

a) 0

b) 0.015

c) 0.034

d) 0.170

e) 0.828

f) Other _____

 

4.iii

What is the correlation coefficient between the number of Oysters and the number of Pearls? (1 decimal accuracy.)

 

a) 999

b) 0

c) 0.1

d) 0.2

e) 0.3

f) 0.4

g) 0.5

h) 0.6

i) 0.7

j) 0.8

k) 0.9

l) 1

m) Other _____

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