ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 50 - 56 of 164

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 = , then x =-1

For median q = , then x = 0

For third quartile q = , then x = 1

The Euler-Maclaurin formula is

where

Given the equation

Let X₁ , X₂ , … , 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 sample, X₁ , X₂ , … , X_n from exponential distribution with mean parameter θ. Then the d…

The characteristic function of X is

Let assume x-µ = v, then dx = dv

Assume that , then dv = λ du

First find the value of this integral, this solution adopts the method of contour integration.

Let assume t > 0, For every n we define in the complex plane the contour C_n is ni

By the residue theorem in the theory of complex we have the function

has in the …

We known that in continuous random variable, the mean is

We know that

dF (x) =-dS (x)

Hence it՚s proofed.

we use Wilcoxon two-sample test to the following data

Let n₁ be the number of breakdown times in the Brand A with median time m₁ , and n₂ the number of breakdown times in the Brand B with median time m₂ . Then the hypothesis is that the median times of the two brands are same against the alternative that they are not same.

For this first arrange the …

To find the mean and variance, we use the conditional expectation and conditional variance

By the given definition of conditional expectation

.

.

.

The variance is