ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 53 - 59 of 165

The characteristic function of X is

Let assume x-µ=v, then dx = dv

We known that in continuous random variable, the mean is

We know that F (x) =1-S (x) and f (x) =dF (x) /dx

dF (x) =-dS (x)

we use Wilcoxon two-sample test to the following data

Let n ₁ be the number of breakdown times in the Brand A with median time m ₁, and n ₂ the number of breakdown times in the Brand B with median time m ₂. Then the hypothesis is that the median times of the two brands are same against the alternative that they are not same.

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

By the given definition of conditional expectation

Let X ~ N (0, σ ²). The density function is

First we find the distribution of Y = X ²

Rewrite the characteristic function Φ (t)

The density function of X is given by Fourier inversion theorem usin

Let the contingent table is

Here A denotes the presence of any attributes and α denotes the absence of attributes A

Since the marginal frequencies is fixed, therefore

Probability for a indivi