Probability-Conditional Probability (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 1 - 6 of 6

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Question number: 1

» Probability » Conditional Probability

Appeared in Year: 2011

Essay Question▾

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Consider the following bivariate p. m. f. of (X, Y):

p (0, 10) = p (0, 20) = 2/18;

p (l, 10) = p (l, 30) = 3/18;

p (1, 20) = p (2, 30) = 4/18;

Obtain the conditional mass functions p (y lx = 2), and p (y lx = 1).

Explanation

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Question number: 2

» Probability » Conditional Probability

Appeared in Year: 2009

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(i) Let X be a random variable such that P [X < 0] = 0 and E [x] exist. Show that P (X ≤ 2E [x] ) ≥ l/2

(ii) Let E [X] = 0 and E [X 2] be finite. Show that P (X 2 < 9E [X 2] ) > 8/9

Explanation

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Question number: 3

» Probability » Conditional Probability

Appeared in Year: 2011

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Let (X, Y) have the uniform distribution over the range 0 < y· < x < 1. Obtain the conditional mean and variance of X given Y = y.

Explanation

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Question number: 4

» Probability » Conditional Probability

Appeared in Year: 2012

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You arc given the following information:

(i) In random testing, you test positive for a disease.

(ii) In 5 % of cases, the test shows positive even when the subject does not have the disease.

(iii) In the population at large, one person in 1000 has the disease. What is the conditional probability that you have the disease given that you have been tested positive, assuming that if someone has the disease, he will test positive with probability 1?

Explanation

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Question number: 5

» Probability » Conditional Probability

Appeared in Year: 2009

Essay Question▾

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The joint density of (X, Y) is

Find the conditional densities and E [X|Y = 1·5].

Explanation

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Question number: 6

» Probability » Conditional Probability

Appeared in Year: 2015

Essay Question▾

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Let X 1, X 2, …, X n be independent Poisson variates with E (X i) =µ i. Find the conditional distribution of

Explanation

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