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Test: Statistics Part:- 1 - Question 1

The standard normal probability function can be approximated as

Where x_{N } = standard normal deviate. If mean and standard deviation of annual precipitation are 102 cm and 27 cm respectively, the probability that the annual precipitation will be between 90 and 102 cm is

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Test: Statistics Part:- 1 - Question 2

Two coins are simultaneously tossed. The probability of two heads simultaneously appearing is

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Test: Statistics Part:- 1 - Question 3

There are two containers, with one containing 4 Red and 3 Green balls and the other containing Blue and 4 Green balls. One bal is drawn at random form each container. The probability that one of the ball is Red and the other is Blue will be

Test: Statistics Part:- 1 - Question 4

A fair coin is tossed three times in succession. If the first toss produces a head, then the probability of getting exactly two heads in three tosses is

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Test: Statistics Part:- 1 - Question 5

Two fair dice are rolled and the sum r of the numbers turned up is considered

Test: Statistics Part:- 1 - Question 6

A box contains 4 white balls and 3 red balls. In succession, two balls are randomly selected and removed from the box. Given that the first removed ball is white, the probability that the second removed ball is red is

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Test: Statistics Part:- 1 - Question 7

X is a uniformly distributed random variable that takes values between 0 and 1. The value of E{X^{3}} will be

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Test: Statistics Part:- 1 - Question 8

Consider a Gaussian distributed random variable with zero mean and standard deviation σ. The value of its cumulative distribution function at the origin will be

Test: Statistics Part:- 1 - Question 9

A random variable is uniformly distributed over the interval 2 to 10. Its variance will be

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Test: Statistics Part:- 1 - Question 10

The probability that there are 53 Sundays in a randomly chosen leap year is

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Test: Statistics Part:- 1 - Question 11

You have gone to a cyber-café with a friend. You found that the cyber-cafe has only three terminals. All terminals are unoccupied. You and your friend have to make a random choice of selecting a terminal. What is the probability that both of you will NOT select the same terminal?

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Test: Statistics Part:- 1 - Question 12

Probability density function p(x) of a random variable x is as shown below. The value of α is

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Test: Statistics Part:- 1 - Question 13

Two dices are rolled simultaneously. The probability that the sum of digits on the top surface of the two dices is even, is

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Test: Statistics Part:- 1 - Question 14

Poisson's ratio for a metal is 0.35. Neglecting piezo-resistance effect, the gage factor of a strain gage made of this metal is

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Test: Statistics Part:- 1 - Question 15

Assume that the duration in minutes of a telephone conversation follows the exponential distribution The probability that the conversation will exceed five minutes is

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Test: Statistics Part:- 1 - Question 16

Using the given data points tabulated below, a straight line passing through the origin is fitted using least squares method. The slope os the line is

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Test: Statistics Part:- 1 - Question 17

The function y = sin φ, (φ > 0) is approximated as y = φ, where φ is in radian. The maximum value of φ for which the error due to the approximation is with in is

Test: Statistics Part:- 1 - Question 18

If two fair coins are flipped and at least one of the outcome is know to be a head, what is the probability that both outcomes are heads?

Test: Statistics Part:- 1 - Question 19

If the difference between the expectation of the square of a random variable ( E [X])^{2} is denoted by R, then

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Test: Statistics Part:- 1 - Question 20

For each element is a set of size 2n, an unbiased coin is tossed. The 2n coin tossed are independent. An element is chosen if the corresponding coin toss were head. The probability that exactly n elements are chosen is

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