# 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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