Probability-Moment and Probability Generating Functions [ISS (Statistical Services) Statistics Paper I]: Questions 5 - 9 of 15

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Question 5

Question MCQ▾

A hen lays eggs, where . Each egg hatches with probability , independently of the other eggs. Find the probability distribution of number of chicks,

Choices

Choice (4)Response

a.

b.

c.

d.

Question does not provide sufficient data or is vague

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Question 6

Question MCQ▾

Suppose that is a random variable taking values in N. The probability generating function of will satisfy the following properties.

Choices

Choice (4)Response

a.

b.

c.

d.

None of the above

Edit

Question 7

Question MCQ▾

If and are independent, then what is the distribution of ?

Choices

Choice (4)Response

a.

b.

c.

d.

None of the above

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Question 8

Appeared in Year: 2022

Question MCQ▾

Consider a Markov chain with state space and transition probabilities given as follows:

Which of the following are true?

Choices

Choice (4)Response

a.

There are infinitely many recurrent classes

b.

Zero is a transient state

c.

The chain has period 2

d.

The chain is irreducible

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Question 9

Appeared in Year: 2022

Question MCQ▾

Let consider a Markov chain on the state space S with transition probability matrix

Then which of the following is always true?

Choices

Choice (4)Response

a.

State 1 has period 2

b.

State 2 is recurrent

c.

State 3 is transient

d.

The chain admits at least two stationary distributions

Edit