ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 55 - 61 of 165

Describe in Detail

The following data represent lifetimes (hours) of batteries for two different brands:

Test whether two brands are the same.

Describe in Detail

Let X ₁, X ₂, ···, X _n be random variables such that

Also

Find

Describe in Detail

Let X ₁, X ₂, …, X _n be independent N (0, σ ²) random variables. Obtain the mean and variance of . What is its probability distribution?

Describe in Detail

Find the density function of X whose characteristic function Φ (t) is given by:

Describe in Detail

For 2X2 table

prove that Chi-square test of independence gives

Describe in Detail

Let X be a random variable with a continuous distribution function F. Show that F (X) has the uniform distribution on (0, 1).

Describe in Detail

For the Cauchy distribution given by

where k is a constant to be suitably chosen, derive the expression for the distribution function. Hence obtain a measure of central tendency and a measure of dispersion. What are the points of inflexion of the distribution?