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 |
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 |
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 |
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 |
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 |