For different sets of datasets X and Y, correlation coefficient between X and Y, that is R and standard deviation of X and Y, that is, S(X) and S(Y) are given in A-D below. Estimate the covariance between X and Y for each dataset and arrange in ascending order.
A. R = 0.5, S(X) = 8, S(Y) = 10
B. R = 4/7, S(X) = 7, S(Y) = 9
C. R = 0.7, S(X) = 12, S(Y) = 5
D. R = 19/42, S(X) = 14, S(Y) = 6
Choose the correct answer from the options given below:डेटासेटों के भिन्न-भिन्न समुच्चयों X व Y हेतु, X व Y के बीच सहसंबंध गुणांक अर्थात् R, तथा X व Y के मानक विचलन अर्थात् S(X) और S(Y) नीचे A-D में दिए गए हैं। प्रत्येक डेटासेट हेतु X व Y के बीच सहप्रसरण (covariance) का आकलन कीजिए और उसे आरोही क्रम में व्यवस्थित कीजिए:
A. R = 0.5, S(X) = 8, S(Y) = 10
B. R = 4/7, S(X) = 7, S(Y) = 9
C. R = 0.7, S(X) = 12, S(Y) = 5
D. R = 19/42, S(X) = 14, S(Y) = 6
नीचे दिए गए विकल्पों में से सही उत्तर चुनिए:

1. AB, A, D, C
2. BC, B, A, D
3. CB, D, A, C
4. DA, C, D, B

Pick an option to check yourself, or open the answer below.

Show answer & explanation

Correct answer: C. B, D, A, C

Explanation

Covariance = R × S(X) × S(Y). A = 0.5×8×10 = 40; B = (4/7)×7×9 = 36; C = 0.7×12×5 = 42; D = (19/42)×14×6 = 38. Ascending order of 36, 38, 40, 42 gives B, D, A, C.सहप्रसरण = R × S(X) × S(Y)। A = 0.5×8×10 = 40; B = (4/7)×7×9 = 36; C = 0.7×12×5 = 42; D = (19/42)×14×6 = 38। 36, 38, 40, 42 का आरोही क्रम B, D, A, C है।