Probability-Elements of Measure Theory (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 1 - 3 of 3

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Question number: 1

» Probability » Elements of Measure Theory

Appeared in Year: 2013

Essay Question▾

Describe in Detail

If the probability for n independent events are p 1, p 2, …, p n, then prove that:

(i) none of the events will occur

(ii) at least one event will occur

(iii) at most one event will occur;

Explanation

Let A 1 , A 2, …, A n, n independent events with probabilities p 1, p 2, …, p n.

(i) Find the probability that none of the events will occur

Since events are independent and the probability that one event does not occur

… (47 more words) …

Question number: 2

» Probability » Elements of Measure Theory

Appeared in Year: 2014

Essay Question▾

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Suppose that all the four outcomes 0 1, 0 2, 0 3 and 0 4 of an experiment are equally likely. Define A = (0 1, 0 4), B = (0 2, 0 4) and C = (0 3, 0 4). What can you say about the pairwise independence and mutually independence of the events A, B and C?

Explanation

Given that there are four outcomes. Define A = (O 1, O 4), B = (O 2, O 4), C = (O 3, O 4)

Their intersection is Equation and Union is AUBUC = (O 1, O 2, O 3, O

… (114 more words) …

Question number: 3

» 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

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