Probability (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 147 - 150 of 205

Get 1 year subscription: Access detailed explanations (illustrated with images and videos) to 458 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: 147

» Probability » Probability Distributions » Joint and Marginal Distributions

MCQ▾

Question

Continuous random variables X and Y have a joint distribution with density function f(x,y)=x2+xy3 for 0<x<1 and 0<y<2 . Find P[X>12 Y>12].

Choices

Choice (4) Response

a.

1316

b.

4364

c.

4352

d.

Question does not provide sufficient data or is vague

Question number: 148

» Probability » Probability Distributions » Gamma

MCQ▾

Question

A chi-square (with n degree of freedom) probability density function satisfies which of the following property/properties?

Choices

Choice (4) Response

a.

If n=2 then f is decreasing with f(0)=1

b.

If 0<n2 , then f is concave downward.

c.

If 0<n<2 , f is increasing with f(x) as x0 .

d.

All a. , b. and c. are correct

Question number: 149

» Probability » Modes of Convergences of Sequences of Random Variables » In Mean Square

MCQ▾

Question

Suppose that (X1,X2,) is a sequence of independent random variables with (X=n3)=1n2 , P(X=0)=11n2 ; nN+ , then the following option is correct?

Choices

Choice (4) Response

a.

XnX almost everywhere

b.

E(Xn)0 as n

c.

XnXasn in probability

d.

Question does not provide sufficient data or is vague

Question number: 150

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

MCQ▾

Question

Consider the following statements and then choose the option in which the given statements are equivalent.

I) P(XnXasn)=0

II) P(XnXasn)=1

III) P( XnX >ϵforinfinitelymanynN+)=1 for every ϵQ+.

IV) P( XnX >ϵforinfinitelymanynN+)=0 for every ϵ>0.

V) P( XkX <ϵforsomekn)0asn for every ϵ>0.

Choices

Choice (4) Response

a.

II and IV

b.

I, III, V

c.

I, V

d.

Question does not provide sufficient data or is vague

Sign In