ISS Statistics Paper I (Old Subjective Pattern): Questions 87 - 92 of 165

Let X be a random variable with mean µ and variance σ ². Then any k > 0, the Chebyshev’s inequality is

or

σ ² = E [X ²] - (E [X] ) ² =4

Then, a lower bound for the probability

Using Chebyshev’s inequality… (2 more words) …

Given that P (A) =1/4, P (B) =1/8, P (C) =1/12

then probability that at least one event of these three events happens is

The events are independent because only one event happens

Let X ₁, X ₂, …, X _m i. i. d. random variables with common p. m. f. is P (X = k) which is a binomail random variables with common parameters n and p respectively. Then, the p. m. f. of S _m = X ₁ +… (117 more words) …

Given that a random sample X ₁, X ₂, …, X _n from N (µ, σ ²) population. The hypothesis is

The null hypothesis is test by chi-square test only assume the sample size is less than 30.

For this we use the likelihood ratio test… (107 more words) …

if X is a continuous random variable and f (x) is a continuous function of X, then f (x) is a probability density function if

Assume but limit is same

This integral is a gamma function

So,

Thus f (x) is a… (57 more words) …

The given differential equation is

with initial condition x ₀ = 0, y ₀ = 1, taking h = 0.05.

Using Euler’s method,

where

So, putting the initial condition, when n = 0

and

Now first modification of y ₁