Probability-Modes of Convergences of Sequences of Random Variables (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 1 - 3 of 11

Get 1 year subscription: Access detailed explanations (illustrated with images and videos) to 404 questions. Access all new questions we will add tracking exam-pattern and syllabus changes. View Sample Explanation or View Features.

Rs. 300.00 or

Question number: 1

» Probability » Modes of Convergences of Sequences of Random Variables » In Distribution

MCQ▾

Question

Suppose that Xn has the discrete uniform distribution on {1n,2n,,n1n,1} for each nN+ and let fn denote the probability density function of Xn. Let X have the continuous uniform distribution on the interval [0, 1] . Then which of the following is correct option?

Choices

Choice (4) Response
a.

P(XnQ)=1 for each n but P(XQ)=0

b.

The distribution of Xn converges to the distribution of X as n

c.

fn(x)0 as n for all x[0, 1]

d. All a. , b. and c. are correct

Question number: 2

» Probability » Modes of Convergences of Sequences of Random Variables » In Distribution

MCQ▾

Question

Suppose that (X1,X2,) is a sequence of random variables (defined on the same probability space) and that the distribution of Xn converges to the distribution of the constant casn . Then________.

Choices

Choice (4) Response
a.

Xnc as n k -th mean

b.

Xnc almost everywhere

c.

Xnc as n in probability

d. All of the above

Question number: 3

» Probability » Modes of Convergences of Sequences of Random Variables » In Distribution

MCQ▾

Question

Consider a random permutation (X1,X2,,Xn) of the elements in the set {1, 2,,n} . We say that s match occurs at position iifXi=i . If Nn denotes the number of matches, then the distribution of Nn converges to ________ as n .

Choices

Choice (4) Response
a.

Exponential distribution with parameter 1

b.

Poisson distribution with parameter 1

c.

Laplace distribution with location parameter 0 and scale parameter 1

d. None of the above

Sign In