Probability (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 64 - 71 of 72
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Question number: 64
» Probability » Standard Probability Distributions » Poisson
Appeared in Year: 2011
Describe in Detail
Show that the sum of two independent Poisson random variables with parameters λ and µ respectively is a Poisson random variable with parameter λ+µ.
Explanation
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Question number: 65
» Probability » Conditional Probability
Appeared in Year: 2009
Describe in Detail
The joint density of (X, Y) is
Find the conditional densities and E [X|Y = 1·5].
Explanation
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Question number: 66
» Probability » Standard Probability Distributions » Normal
Appeared in Year: 2011
Describe in Detail
Let the joint p. d. f. of (X, Y) be f (x, y) = e -y, 0 < x < y < ∞.
Obtain the probability P (X + Y ≤ 1).
Explanation
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Question number: 67
» Probability » Probability Generating Functions
Appeared in Year: 2009
Describe in Detail
Find the generating function of X whose probability density function is
P [X = r] =pq r-1, r = 1, 2, …, 0 < p < 1, q = 1 - p
Explanation
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Question number: 68
» Probability » Standard Probability Distributions » Exponential
Appeared in Year: 2009
Describe in Detail
Explain “Memoryless property” of a distribution. Show that the exponential distribution has memoryless property.
Explanation
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Question number: 69
» Probability » Expectation
Appeared in Year: 2015
Describe in Detail
For random variables X, Y, show that
Explanation
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Question number: 70
» Probability » Conditional Probability
Appeared in Year: 2015
Describe in Detail
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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Question number: 71
» Probability » Laws of Total and Compound Probability
Appeared in Year: 2011
Describe in Detail
Verify the following identities:
(i)
(ii)
Explanation
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