ISS Statistics Paper I (New 2016 MCQ Pattern): Questions 376 - 378 of 404

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Question number: 376

» Probability » Characteristic Function

MCQ▾

Question

For any random variable X , its characteristic function X(.) is uniformly continuous on R and satisfies following properties________ always.

Choices

Choice (4) Response

a.

X(t)=X(t)¯ , where for z a complex number, z¯ denote the conjugate.

b.

X(t)1

c.

X(0)=12

d.

None of the above

Question number: 377

» Probability » Laws of Large Numbers

MCQ▾

Question

Let X1,X2, be a sequence of independent, identically distributed random variables, each having finite mean μ=E(Xk),k=1, 2,.. . Then, which of the following option is/are correct according to statement of Strong law of large number?

Choices

Choice (4) Response

a.

P{limnX1++Xnn=μ}=1

b.

limnP{ X1++Xnnμ ε}=0

c.

None of the above

d.

All of the above

Question number: 378

» Probability » Central Limit Theorems for Independent Variables

MCQ▾

Question

The amount of regular unleaded gasoline purchased every week at a gas station near Palampur follows the normal distribution with mean 50000 gallons and standard deviation 10000 gallons. The starting supply of gasoline is 74000 gallons, and there is a scheduled weekly delivery of 47000 gallons. Find the probability that, after 11 weeks, the supply of gasoline will be below 20000 gallons.

Choices

Choice (4) Response

a.

0.2643

b.

0.7357

c.

0.8944

d.

0.1056

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