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

Essay Question▾

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

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: 66

» Probability » Standard Probability Distributions » Normal

Appeared in Year: 2011

Essay Question▾

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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

… (61 more words) …

Question number: 67

» Probability » Probability Generating Functions

Appeared in Year: 2009

Essay Question▾

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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

Essay Question▾

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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

Essay Question▾

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For random variables X, Y, show that

Explanation

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Question number: 70

» Probability » Conditional Probability

Appeared in Year: 2015

Essay Question▾

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

Essay Question▾

Describe in Detail

Verify the following identities:

(i)

(ii)

Explanation

… (60 more words) …

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