The mean of the data \( 4,10,5,9,12 \) is - \( \begin{array}{llll}\text { (A) } 8 & \text { (B) } 10 & \text { (C) } 9 & \text { (D) } 15 \\ 52 \text { ताश के पत्तों में से एक पत्ता निकाला जाता है, तो रानी आने की प्रायिकता है - } \\ \begin{array}{llll}\text { (अ) } \frac{1}{26} & \text { (ब) } \frac{1}{13} & \text { (स) } \frac{4}{53} & \text { (द) } \frac{4}{13}\end{array} \\ \text { A card is drawn from the set of } 52 \text { cards, then the probability of getting a queen is } \\ \begin{array}{llll}\text { (A) } \frac{1}{26} & \text { (B) } \frac{1}{13} & \text { (C) } \frac{4}{53} & \text { (D) } \frac{4}{13}\end{array} \\ \begin{array}{ll}\text { Page } 2 \text { of } 4 & \end{array}\end{array} \).

Question 19. [ \( 5 \times 1 \) ] In sub part (i) and (ii) choose the correct option and sub-part (iii) to (v) answer the questions as instructed. (i) If the correlation coefficient between two variable is 1, then two least square lines of regression are: (a) parallel (b) perpendicular (c) coincident (d) both (a) and (c) (ii) Read the following statement and choose the correct option: (I) if \( b_{x y} \cdot b_{y x}=1 \), then the regression lines are perpendicular (II) If \( b_{x y} b_{y x}=0 \), then the regression lines are perpendicular (III) If \( b_{x y}+b_{y x}=0 \), then the regression lines are perpendicular (IV) \( \quad b_{x y}+b_{y x}=1 \), then the regression lines are perpendicular Which of the following is correct? (a) Only (II) is correct (b) Only (II) and (III) are correct (c) Only (I) and (IV) are correct (d) Only (I) is correct (iii) If the two line of regression are \( 3 x-2 y+1=0 \) and \( 2 x-y-2=0 \), then find the mean of \( x \) and mean of \( y \). (iv) A teacher asked his student to find the value of coefficient of correlation where two coefficient of regression are -0.3 and -1.2 . Fahad said the value of coefficient of correlation is \( \pm 0.6 \) Janhavi said the value of coefficient of correlation is - 0.6 How is correct? Justify your answer. (v) Find the value of \( b_{x y} \) for five observations of pairs( \( \left.\mathrm{x}, \mathrm{y}\right) \sum x=15, \sum y=25, \sum y^{2}= \) 135 and \( \sum x y=83 \). Question 19. [2] The equation of two line of regression are \( 2 x+3 y-6=0 \) and \( 5 x+7 y-12=0 \). Find the value of coefficient of correlation. Question 20. [4] The following observations are given: \[ (1,4),(2,8),(3,2)(4,12)(5,10),(6,14),(7,16)(8,6),(9,18) \] Estimate the value of \( y \) when the value of \( x \) is 10 Question 21. [4] The coefficient of correlation between the value denoted by \( X \) and \( Y \) is 0.5 . The mean of \( X \) is 3 and that of \( Y \) is 5 . Their standard deviation is 5 and 4 respectively. Find (i) The two line of regression (ii) The expected value of \( X \), when \( Y \) is given 9.

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