Probability [ISS (Statistical Services) Statistics Paper I]: Questions 139 - 143 of 212

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Question 139

Question MCQ▾

Continuous random variables and have a joint distribution with density function for and . Find

Choices

Choice (4)Response

a.

b.

c.

d.

All of the above

Edit

Question 140

Question MCQ▾

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

Choices

Choice (4)Response

a.

If then is decreasing with

b.

If , then is concave downward.

c.

If , is increasing with as .

d.

All a., b. and c. are correct

Edit

Question 141

Question MCQ▾

Suppose that is a sequence of independent random variables with , ; , then the following option is correct?

Choices

Choice (4)Response

a.

in probability

b.

almost everywhere

c.

as

d.

Question does not provide sufficient data or is vague

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Question 142

Question MCQ▾

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

I)

II)

III) for every

IV) for every

V) for every

Choices

Choice (4)Response

a.

II and IV

b.

I, III, V

c.

I, V

d.

None of the above

Edit

Question 143

Question MCQ▾

If has the distribution with degrees of freedom in the numerator and degrees of freedom in the denominator then, will follow ________ distribution.

Choices

Choice (4)Response

a.

b.

with degrees of freedom.

c.

d.

All of the above

Edit