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प्रश्न
Examine whether the following statement pattern is tautology, contradiction or contingency :
p ∨ – (p ∧ q)
उत्तर
We make the truth table as follows
| P | q | P ∧ q | – (P ∧ q) | Pv – (P ∧ q) |
| T | T | T | F | T |
| T | F | F | T | T |
| F | T | F | T | T |
| F | F | F | T | T |
So the final statement is always true. So it is a
tautology.
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संबंधित प्रश्न
The regression equation of y on x is given by 3x + 2y - 26 = O. Find byx.
Bring out the inconsistency; if any: byx + bxy = 1.30. and r = 0.75
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From the two regression equations y = 4x - 5 and 3x = 2y + 5, find `barx and bary`
From the data 7 pairs of observations on X and Y following results are obtained :
∑(xi - 70) = - 38 ; ∑ (yi - 60) = - 5 ;
∑ (xi - 70)2 = 2990 ; ∑ (yi - 60)2 = 475 ;
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(a) The line of regression of Y on X.
(b) The line of regression of X on Y.
Find the line of best fit for the following data, treating x as the dependent variable (Regression equation x on y):
| X | 14 | 12 | 13 | 14 | 16 | 10 | 13 | 12 |
| Y | 14 | 23 | 17 | 24 | 18 | 25 | 23 | 24 |
Hence, estimate the value of x when y = 16.
A psychologist selected a random sample of 22 students. He grouped them in 11 pairs so that the students in each pair have nearly equal scores in an intelligence test. In each pair, one student was taught by method A and the other by method B and examined after the course. The marks obtained by them after the course are as follows:
| Pairs | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| Methods A | 24 | 29 | 19 | 14 | 30 | 19 | 27 | 30 | 20 | 28 | 11 |
| Methods B | 37 | 35 | 16 | 26 | 23 | 27 | 19 | 20 | 16 | 11 | 21 |
Calculate Spearman’s Rank correlation.
The coefficient of correlation between the values denoted by X and Y is 0.5. The mean of X is 3 and that of Y is 5. Their standard deviations are 5 and 4 respectively.
Find:
(i) the two lines of regression.
(ii) the expected value of Y, when X is given 14.
(iii) the expected value of X, when Y is given 9.
If the regression line of x on y is, 9x + 3y − 46 = 0 and y on x is, 3x + 12y − 7 = 0, then the correlation coefficient ‘r’ is equal to:
For 5 observations of pairs (x, y) of variables X and Y, the following results are obtained:
∑x = 15, ∑y = 25, ∑x2 = 55, ∑y2 = 135, ∑xy = 83.
Calculate the value of bxy and byx.
The following table shows the Mean, the Standard Deviation and the coefficient of correlation of two variables x and y.
| Series | x | y |
| Mean | 8 | 6 |
| Standard deviation | 12 | 4 |
| Coefficient of correlation | 0.6 | |
Calculate:
- the regression coefficient bxy and byx
- the probable value of y when x = 20
