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 _____
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
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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