Probability (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 27 - 32 of 72

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Question number: 27

» Probability » Standard Probability Distributions » Uniform

Appeared in Year: 2010

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Let X be a random variable with a continuous distribution function F. Show that F (X) has the uniform distribution on (0, 1).

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Question number: 28

» Probability » Standard Probability Distributions » Cauchy

Appeared in Year: 2012

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For the Cauchy distribution given by

where k is a constant to be suitably chosen, derive the expression for the distribution function. Hence obtain a measure of central tendency and a measure of dispersion. What are the points of inflexion of the distribution?

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Question number: 29

» Probability » Sample Space

Appeared in Year: 2011

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A fair die is thrown until a 6 appears. Specify the sample space. What is the probability that it must be thrown at least 3 times?

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Question number: 30

» Probability » Conditional Probability

Appeared in Year: 2011

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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).

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Question number: 31

» Probability » Distribution Function » Standard Probability Distributions

Appeared in Year: 2010

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Let (X, Y) be jointly distributed with p. d. f.

Find marginal probability density function of X and Y.

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Question number: 32

» Probability » Tchebycheffs Inequality

Appeared in Year: 2011

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Let X be a positive valued random variable. Prove that

Hence deduce the Chebychev’s inequality.

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