ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 12 - 17 of 164

The probability of purchases a ticket is

First prize amount is 1000

Two second prizes amount is 500 each

Three third prizes amount is 100 each

X denotes the amount he may get

Then, the expected value of X is

The variance of X is

Given that a = 1,

The mean is

The standard deviation is

Measure of skewness

The property of memory less is that these distributions of ″ time from now to the next period ″ are exactly the same. The property is most easily explained in terms of ″ waiting times.

Suppose X is a discrete random variable whose values is a non-negative. In probability theory, a distribution is said to have lack of memory if

Geometric distribution …

Let x_{(1) ,} x_{(2) , … ,} x_(n) be the ordered sample values from a population F (X) and M be its median.

Here we test where M₀ is the given value of the median and hence

To perform the sign test, first find the differences (X_(i) -M₀) for i = 1,2, … , n and consider their signs. Suppose the number of + ve sign is r and negative sign is (n-r) . For this w…

Let X and Y are two independent chi-squared random variables with degree of freedom n and m respectively. We proof this by moment generating function. The moment generating function of chi-squared distribution is

Then moment generating function of sum of two random variable (X + Y) is

because X and Y are independent

‎

which is the moment generating fu…

Let x denote the time Amal arrives at the bar and y denote the time Bimal arrives at the bar from 6 p. m. We will draw the lines y = x – 10 and y = x + 10 and shade the area in between these two lines to denote the event.

They will meet if that is (x, y) falls in the shaded region. The area of total is 3600 but the total u…