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Evaluate the following limit:
`lim_(x->5)[(x^3 -125)/(x^5 - 3125)]`
Concept: undefined >> undefined
Evaluate the following limit:
`lim_(x ->7)[((root3x - root3(7))(root3x + root3(7)))/(x - 7)]`
Concept: undefined >> undefined
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Evaluate the following limit:
`lim_(x->-2)[(x^7 + x^5 + 160)/(x^3 + 8)]`
Concept: undefined >> undefined
Find the various and S.D. for the following set of numbers.
7, 11, 2, 4, 9, 6, 3, 7, 11, 2, 5, 8, 3, 6, 8, 8, 8, 2, 6
Concept: undefined >> undefined
Find the various and S.D. for the following set of numbers.
65, 77, 81, 98, 100, 80, 129
Concept: undefined >> undefined
Compute variance and standard deviation for the following data:
| x | 2 | 4 | 6 | 8 | 10 |
| f | 5 | 4 | 3 | 2 | 1 |
Concept: undefined >> undefined
Compute the variance and S.D.
| x | 1 | 3 | 5 | 7 | 9 |
| Frequency | 5 | 10 | 20 | 10 | 5 |
Concept: undefined >> undefined
Following data gives age of 100 students in a school. Calculate variance and S.D.
| Age (In years) | 10 | 11 | 12 | 13 | 14 |
| No. of students | 10 | 20 | 40 | 20 | 10 |
Concept: undefined >> undefined
The mean and variance of 5 observations are 3 and 2 respectively. If three of the five observations are 1, 3 and 5, find the values of other two observations.
Concept: undefined >> undefined
Obtain standard deviation for the following date:
| Height (in inches) | 60 – 62 | 62 – 64 | 64 – 66 | 66 – 68 | 68 – 70 |
| Number of students | 4 | 30 | 45 | 15 | 6 |
Concept: undefined >> undefined
The following distribution was obtained change of origin and scale of variable X.
| di | – 4 | – 3 | – 2 | – 1 | 0 | 1 | 2 | 3 | 4 |
| fi | 4 | 8 | 14 | 18 | 20 | 14 | 10 | 6 | 6 |
If it is given that mean and variance are 59.5 and 413 respectively, determine actual class intervals.
Concept: undefined >> undefined
Following tale gives income (X) and expenditure (Y) of 25 families:
| Y/X | 200 – 300 | 300 – 400 | 400 – 500 |
| 200 – 300 | IIII I | IIII I | I |
| 300 – 400 | – | IIII | IIII I |
| 400 – 500 | – | – | II |
Find Conditional frequency distribution of X when Y is between 300 – 400.
Concept: undefined >> undefined
Following tale gives income (X) and expenditure (Y) of 25 families:
| Y/X | 200 – 300 | 300 – 400 | 400 – 500 |
| 200 – 300 | IIII I | IIII I | I |
| 300 – 400 | – | IIII | IIII I |
| 400 – 500 | – | – | II |
Find Conditional frequency distribution of Y when X is between 200 – 300.
Concept: undefined >> undefined
Following data gives height in cm (X) and weight in kgs (Y) of 20 boys. Prepare a bivariate frequency table taking class intervals 150-154, 155-159...etc. for X and 35-39, 40-44 ...etc. for Y. Also find conditional frequency distribution of Y when 155 ≤ X ≤ 159
(152, 40) (160, 54) (163, 52) (150, 35) (154, 36) (160, 49) (166, 54) (157, 38) (159, 43) (153, 48) (152, 41) (158, 51) (155, 44) (156, 47) (156, 43) (166, 53) (160, 50) (151, 39) (153, 50) (158, 46)
Concept: undefined >> undefined
Find correlation coefficient between x and y series for the following data.
n = 15, `bar"x"` = 25, `bar"y"` = 18, σx = 3.01, σy = 3.03, `sum("x"_"i" - bar"x") ("y"_"i" - bar"y")` = 122
Concept: undefined >> undefined
The correlation coefficient between two variables x and y are 0.48. The covariance is 36 and the variance of x is 16. Find the standard deviation of y.
Concept: undefined >> undefined
In the following data one of the value y of is missing. Arithmetic means of x and y series are 6 and 8 respectively. `(sqrt(2) = 1.4142)`
| x | 6 | 2 | 10 | 4 | 8 |
| y | 9 | 11 | ? | 8 | 7 |
Calculate the correlation coefficient
Concept: undefined >> undefined
Find correlation coefficient from the following data. `["Given:" sqrt(3) = 1.732]`
| x | 3 | 6 | 2 | 9 | 5 |
| y | 4 | 5 | 8 | 6 | 7 |
Concept: undefined >> undefined
Correlation coefficient between x and y is 0.3 and their covariance is 12. The variance of x is 9, Find the standard deviation of y.
Concept: undefined >> undefined
A letter lock has 3 rings and each ring has 5 letters. Determine the maximum number of trials that may be required to open the lock.
Concept: undefined >> undefined
