# Probability (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 14 - 19 of 72

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## Question number: 14

» Probability » Probability Generating Functions

Appeared in Year: 2009

### Describe in Detail

Given the distribution function

find its probability density function.

### Explanation

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## Question number: 15

» Probability » Convergence » In Distribution

Appeared in Year: 2013

### Describe in Detail

Show that convergence in probability implies convergence in distribution.

### Explanation

… (60 more words) …

## Question number: 16

» Probability » Probability of M Events Out of N

Appeared in Year: 2009

### Describe in Detail

A die is rolled twice. Let A, B, C denote the events respectively that the sum of scores is 6, the sum of scores is 7, and the first score is 4. Are A and C independent? Are B and C independent?

### Explanation

… (77 more words) …

## Question number: 17

» Probability » Tchebycheffs Inequality

Appeared in Year: 2013

### Describe in Detail

Let X be a random variable with E [X] = 4 and E [X ^{2}] = 20. Use Chebyshev’s inequality to determine a lower bound for the probability P [0 < x < 8].

### Explanation

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## Question number: 18

» Probability » Probability Generating Functions

Appeared in Year: 2014

### Describe in Detail

Let P (s) be the probability generating function associated with a non-negative, integer valued random variable X. Show that

### Explanation

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## Question number: 19

» Probability » Bayes' Theorem

Appeared in Year: 2014

### Describe in Detail

There are three identical bags U _{1}, U _{2} and U _{3}. U _{1} contains 3 red and 4 black balls; U _{2} contains 4 red and 5 black balls; U _{3} contains 4 red and 4 black balls. One bag is chosen at random; a ball is drawn at random from the chosen bag and it is found to be red. Find the probability that the first bag is chosen.

### Explanation

… (74 more words) …