ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 47 - 52 of 165

The method of calculating the association between the ranks is known as Spearman’s rank correlation. The candidates are rank by the UPSC examination taken for two papers which is independent. The Spearman’s rank correlation is

where n is the number of candidates and d _i is the difference between the rank of the i

This proof is a lack of memory property. We known that

Therefore ………… (1)

The equation is

Using equation (1)

The seven ordinates of the integrand using Simpson’s rule is

Where h = 1/6 (b-a) and y _k =f (a + kh) for k = 0,1, 2,3, 4,5, 6

Here, b = 1, a = 0, h = 1/6, f (x) =

For find the median and quartile of the Cauchy distribution, q is any quartile. Then, for which value of q, the x value is

For first quartile q = 1/4, then x=-1

For median q =

The Euler-Maclaurin formula is

where

Given the equation

Let X ₁, X ₂, …, X _n, be n independently identically distributed random variables following an exponential distribution with mean parameter θ. The probability density and distribution function is

Let X ₍₁₎ , X ₍₂₎ , …, X _(n) denote the order statistic of a random