The milk yield, in litres, of 10 cows in a herd in a week is as given below:
18, 21, 20, 17, 24, 22, 16, 25, 15, 20
Compute the first three moments about the mean and the skewness for the data given above.
To compute the first three moments about the mean and the skewness for the given data, follow these steps:
Step 1: Calculate the Mean (μ) of the data set:
μ = (18 + 21 + 20 + 17 + 24 + 22 + 16 + 25 + 15 + 20) / 10
μ = 198 / 10
μ = 19.8 liters
Step 2: Calculate the first moment about the mean (Raw Moment):
The first moment about the mean is given by:
M₁ = Σ(xi - μ), for all data points xi
M₁ = (18 - 19.8) + (21 - 19.8) + (20 - 19.8) + (17 - 19.8) + (24 - 19.8) + (22 - 19.8) + (16 - 19.8) + (25 - 19.8) + (15 - 19.8) + (20 - 19.8)
M₁ = (-1.8) + (1.2) + (0.2) + (-2.8) + (4.2) + (2.2) + (-3.8) + (5.2)
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Let X and Y have the continuous joint distribution with p.d.f.
where a > 0.Compute the marginal densities of X and Y. Check whether X and Y are independent.
The milk yield, in litres, of 10 cows in a herd in a week is as given below:
18, 21, 20, 17, 24, 22, 16, 25, 15, 20
Compute the first three moments about the mean and the skewness for the data given above.
Let X be a r.v. with p.m.f. given by the following table:
| - 2 | - 1 | 0 | 1 | 2 |
| 3 20 | 4 20 | 6 20 | 4 20 | 3 20 |
6 observations on (X,Y) yielded the following data:
i) Determine the correlation coefficient between X and Y.
ii) Given X =10 , what will be the predicated value of Y?
iii) Given Y = 15, predict X.
Prove that
for all m > 0, n > 0.Hence evaluate (10,7) and
.
Let X1 ,X2 ,...,Xn be a random sample from a normal population, N(.Obtain a (1-
) level confidence interval for
when
is unknown.
If a random variable U has the t-distribution with n degrees of freedom, show that Z = U2 has the F-distribution with 1 and n degrees of freedom.