Probability (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 176 - 179 of 205

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Question number: 176

» Probability » Tchebycheff's Inequalities

MCQ▾

Question

If Equation follows an exponential distribution with Equation , then what is the bound of Equation using Tchebycheff’s Inequality?

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

Question number: 177

» Probability » Characteristic Function

MCQ▾

Question

For any random variable Equation , its characteristic function Equation is uniformly continuous on Equation and satisfies following properties________ always.

Choices

Choice (4) Response

a.

Equation , where for Equation a complex number, Equation denote the conjugate.

b.

Equation

c.

Equation

d.

None of the above

Question number: 178

» Probability » Laws of Large Numbers

MCQ▾

Question

Let Equation be a sequence of independent, identically distributed random variables, each having finite mean Equation . Then, which of the following option is/are correct according to statement of Strong law of large number?

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

None of the above

d.

All of the above

Question number: 179

» 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 Equation gallons and standard deviation Equation gallons. The starting supply of gasoline is Equation gallons, and there is a scheduled weekly delivery of Equation gallons. Find the probability that, after Equation weeks, the supply of gasoline will be below Equation gallons.

Choices

Choice (4) Response

a.

0.2643

b.

0.7357

c.

Equation

d.

0.1056

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