Probability (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 46 - 52 of 72

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Question number: 46

» Probability » Convergence » In Distribution

Appeared in Year: 2014

Essay Question▾

Describe in Detail

{X n} is a sequence of independent variables. Show that

where X is a random variable. Is the converse true?

Explanation

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Question number: 47

» Probability » Distribution Function » Standard Probability Distributions

Appeared in Year: 2010

Essay Question▾

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Let k > 0 be a constant, and

Obtain P (X > 0.3).

Explanation

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Question number: 48

» Probability » Probability of M Events Out of N

Appeared in Year: 2010

Essay Question▾

Describe in Detail

A unbaised die is rolled twice. Let A be the event that the first throw shows a number ≤ 2, and B be the event that the second throw shows at least 5. Show that P (AUB) =5/9.

Explanation

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Question number: 49

» Probability » Tchebycheffs Inequality

Appeared in Year: 2009

Essay Question▾

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Let X ~ BIN (100, 0·2). Compute P [10 ≤ X ≤ 30].

Explanation

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Question number: 50

» Probability » Definitions and Axiomatic Approach

Appeared in Year: 2013

Essay Question▾

Describe in Detail

Let X have the density function,

(i) Find the constant c.

(ii) Find the distribution function.

(iii) Compute P [X > -1/2].

Explanation

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Question number: 51

» Probability » Standard Probability Distributions » Geometric

Appeared in Year: 2012

Essay Question▾

Describe in Detail

Write down the probability mass function of geometric distribution. State and prove its ‘lack of memory property’. Find also the mean and the variance of the distribution.

Explanation

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Question number: 52

» Probability » Standard Probability Distributions » Normal

Appeared in Year: 2014

Essay Question▾

Describe in Detail

If f x (x) be the probability density function of a N (µ, σ 2) distribution, then show that

where , and φ (x) and Φ (x) are the probability density function and distribution function of the standard normal distribution respectively.

Explanation

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