Question

From a box of fruit containing 47 oranges and 1 apple a random sample of 2 pieces of fruit has been selected without replacement. Let X be the number of oranges and Y be the number of apples in the sample. What will the correlation of X and Y be?  

(Hint the variance of X and Y same.

Covariance is just negative of these variances. )

Answer 1

The correlation between X and Y is -1. [ANSWER]

Explanation:

Since, out of a box containing 47 oranges and 1 apple, we draw a sample (without replacement) of size 2. And since in that sample of size 2, X is the number of oranges and Y is the number of apples. Thus, clearly:

X + Y = 2

=> Y = 2 - X

From the above equation we see that X and Y have a perfectly negatively linear relationship and thus we can conclude that the correlation between X and Y is -1.

Another way to find the value of the correlation is to consider:

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