Test: Statistics Part:- 1 - Mathematics MCQ

# Test: Statistics Part:- 1 - Mathematics MCQ

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## 20 Questions MCQ Test Additional Topics for IIT JAM Mathematics - Test: Statistics Part:- 1

Test: Statistics Part:- 1 for Mathematics 2024 is part of Additional Topics for IIT JAM Mathematics preparation. The Test: Statistics Part:- 1 questions and answers have been prepared according to the Mathematics exam syllabus.The Test: Statistics Part:- 1 MCQs are made for Mathematics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Statistics Part:- 1 below.
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Test: Statistics Part:- 1 - Question 1

### The standard normal probability function can be approximated as Where xN  = 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

Detailed Solution for Test: Statistics Part:- 1 - Question 1

Here μ = 102 cm and σ = 27 cm

This area is shown below

The shaded area in above figure is given by F(0) - F(-0.44)

= 0.5 - 0.3345
= 0.1655 = 16.55%

Test: Statistics Part:- 1 - Question 2

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

Detailed Solution for Test: Statistics Part:- 1 - Question 2

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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

Detailed Solution for Test: Statistics Part:- 1 - Question 4

After first head in first toss, probability of tails in 2nd and 3rd toss = 1/2.1/2 = 1/4
∴ Probability of exactly two heads = 1 - 1/4 = 3/4

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

Detailed Solution for Test: Statistics Part:- 1 - Question 6

After first ball is drawn white then sample space has 4 + 3 – 1 = 6 balls.
Probability of second ball is red without replacement

Test: Statistics Part:- 1 - Question 7

X is a uniformly distributed random variable that takes values between 0 and 1. The value of E{X3} will be

Detailed Solution for Test: Statistics Part:- 1 - Question 7

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

Detailed Solution for Test: Statistics Part:- 1 - Question 9

= 16/3

Test: Statistics Part:- 1 - Question 10

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

Detailed Solution for Test: Statistics Part:- 1 - Question 10

No. of days in a leap year are 366 days. In which there are 52 complete weeks and 2 days extra.
This 2 days may be of following combination.
1. Sunday & Monday
2. Monday & Tuesday
3. Tuesday & Wednesday
4. Wednesday & Thursday
5. Thursday & Friday
6. Friday & Saturday
7. Saturday & Sunday
There are two combination of Sunday in (1.) and (7).
∴ Required probability
= 2/7

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?

Detailed Solution for Test: Statistics Part:- 1 - Question 11

Out of three terminals probability of selecting terminals of two friends is  = 1/3
∴ Probability of not selecting same terminal = 1- 1/3 = 2/3

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

Detailed Solution for Test: Statistics Part:- 1 - Question 12

From, figure, area of traiangle = 1/2.c.α = αc/2

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

Detailed Solution for Test: Statistics Part:- 1 - Question 13

Here sample space S = 6 x 6 = 36
Total no. of way in which sum of digits on the top surface of the two dice is even is 18.
∴ The require probability = 18/36 = 0.5.

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

Detailed Solution for Test: Statistics Part:- 1 - Question 14

Poission's ratio σ = 0.36
Gage factor, Gr = 1 + 2σ = 1 + 2 x 0.35 = 1.70

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

Detailed Solution for Test: Statistics Part:- 1 - Question 15

Required probability =

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

Detailed Solution for Test: Statistics Part:- 1 - Question 16

Suppose the line being, y = mx
Since, it has been fit by least square method, therefore
∑ y = μ ∑ x, and ∑ x y = μ ∑ x2
∴ m = 1.1

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

Detailed Solution for Test: Statistics Part:- 1 - Question 19

We know,
The second control momnt,
μ2 = E{X-m)}2 [m = mean of the distribution of X]
= E(X2)−2m×E(X) + m2
= E(X2)−2[E(X)]2 + E(X) [∴ m = E(X)]
E (X2) − [E ( X)]2

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

Detailed Solution for Test: Statistics Part:- 1 - Question 20

The probability that exactly n elements are chosen = the probability of getting n heads out of 2n tosses

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