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

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Question number: 87

» Probability » Tchebycheffs Inequality

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Let X be a random variable with E [X] = 3 and E [X 2] = 13. Use Chebyshev’s inequality to obtain P [-2 < X < 8].

Explanation

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

Equation

or Equation

σ 2 = E [X 2] - (E [X] ) 2 =4

Then, a lower bound for the probability

Equation

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

Question number: 88

» Probability » Elements of Measure Theory

Appeared in Year: 2012

Essay Question▾

Describe in Detail

Of three independent events A, Band C, A only happens with probability ¼, B only happens with probability 1/8 and C only happens with probability 1/12. Find the probability that at least one of these three events happens.

Explanation

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

Equation

Equation

Equation

The events are independent because only one event happens

Equation

Equation

Equation

Equation

Question number: 89

» Probability » Standard Probability Distributions » Binomial

Appeared in Year: 2010

Essay Question▾

Describe in Detail

Let X 1, X 2, …, X m be i. i. d. random variables with common p. m. f.

Equation

obtain the p. m. f. of S m = X 1 + X 2 + …. + X m.

Explanation

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) …

Question number: 90

» Statistical Methods » Tests of Significance » Chi-Square

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Explain how to carry out the chi-squared test for Equation on the basis of a random sample

X 1, X 2, …, X n from N (µ, σ 2) population.

Explanation

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

Equation

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) …

Question number: 91

» Probability » Standard Probability Distributions » Gamma

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Let

Equation

Show that f (x) is a probability density function. Obtain V (X).

Explanation

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

Equation

Equation

Equation

Assume Equation but limit is same

Equation

Equation

This integral is a gamma function Equation

So,

Equation

Thus f (x) is a… (57 more words) …

Question number: 92

» Numerical Analysis » Summation Formula » Euler-Maclaurin's

Appeared in Year: 2014

Essay Question▾

Describe in Detail

Using Euler’s method, compute the values of y correct upto 4 places of decimal for the differential equation Equation with initial condition x 0 = 0, y 0 = 1, taking h = 0.05.

Explanation

The given differential equation is

Equation

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

Using Euler’s method,

Equation

where

Equation

So, putting the initial condition, when n = 0

Equation

Equation

Equation

and

Equation

Equation

Now first modification of y 1

Equation

Equation<span class="more">… (25 more words) …</span>

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