# 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

### 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

### Describe in Detail

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

### 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

### Describe in Detail

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

### 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

### 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

### 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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