Test: Probability and Statistics - 5

# Test: Probability and Statistics - 5

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## 20 Questions MCQ Test Topic-wise Tests & Solved Examples for IIT JAM Mathematics | Test: Probability and Statistics - 5

Test: Probability and Statistics - 5 for Mathematics 2022 is part of Topic-wise Tests & Solved Examples for IIT JAM Mathematics preparation. The Test: Probability and Statistics - 5 questions and answers have been prepared according to the Mathematics exam syllabus.The Test: Probability and Statistics - 5 MCQs are made for Mathematics 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Probability and Statistics - 5 below.
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Test: Probability and Statistics - 5 - Question 1

### From a pack of 52 cards two are drawn at random. What is the probability that one is a king and the other a queen?

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Test: Probability and Statistics - 5 - Question 2

### The probability that the sum of two numbers x and y randomly chosen in the interval (0, 1) greater than 1 while the sum of the squares less than 1 is equal to

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Test: Probability and Statistics - 5 - Question 3

### If the probabilities that A and B will die within a year are p and q respectively, what is the probability that only one of them will be alive at the end of the year?

Detailed Solution for Test: Probability and Statistics - 5 - Question 3

(1 - p ) q + (1 - q) p = p + q 2 pq

Test: Probability and Statistics - 5 - Question 4

The probability that a number selected at random between 100 and 999 (both inclusive) will not contain the digit 3 is

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Test: Probability and Statistics - 5 - Question 5

At a railway station a passenger leaves his luggage in a locker which is opened by dialling a three-digit code. The passenger chooses the code, closes the locker and leaves for the town. A stranger who does not know the code tries to open the locker by dialling three digits at random without repeating the unsuccessful codes. The probability that the stranger does not have to perform more than 100 trials for a success is

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Test: Probability and Statistics - 5 - Question 6

What is the probability of getting seventh head in the tenth toss of an unbiased coin.

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Note: In the first 9 tosses any 6 gives head but 10th toss result into head only.

Test: Probability and Statistics - 5 - Question 7

A committee of 5 is to be chosen from a group of 9 people. What is the probability that a certain married couple will either serve together or not at all?

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Test: Probability and Statistics - 5 - Question 8

What is the probability that the product of two parts of 2n is greater than the 3/4 of their maximum product.

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Test: Probability and Statistics - 5 - Question 9

What is the probability that an urn containing 5 balls contains only white balls if the first two balls drawn from it was found to be white

Detailed Solution for Test: Probability and Statistics - 5 - Question 9

This conditional probability is equal

Test: Probability and Statistics - 5 - Question 10

If the probabilities that A and B will die within a year are p and q respectively, then the probability that only one of them will be alive at the end of the year is

Detailed Solution for Test: Probability and Statistics - 5 - Question 10

p (1- q) + q(l - p ) = p + q - 2 pq.

Test: Probability and Statistics - 5 - Question 11

It is known that the samples 3.1, 0.2., 1,6, 5.2 and 2.1 are from a random variable that is uniformly distributed over the unknown range (α, β) Find the maximum likelihood estimates for the parameters α and β

Detailed Solution for Test: Probability and Statistics - 5 - Question 11

α ((0.2, 5.2); minimum to maximum value.

Test: Probability and Statistics - 5 - Question 12

We make n independent trials in each of which an event A may occur with probability p. A random variable X is defined as the number of occurrences of the event A in all the n trials. The variance of X is

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Test: Probability and Statistics - 5 - Question 13

X is a continuous random variate with pdf  Defining Y = X +  1, E[Y] is found to be

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is probability density* of standard normal distribution
N(0, 1), so E (X) = 0
Y = X +1 ⇒ E{Y) = E(X + 1) = E{X) + 1 = 1

Test: Probability and Statistics - 5 - Question 14

If X is uniformly distributed random variable over the interval (1, 4), the probability V < 0, where Y = X2 - 4 is

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so in interval (1, 4) of length 3 we have interval (1, 2) of length 1 in our favour. So probability required = 1/3.

Test: Probability and Statistics - 5 - Question 15

Let X be a poisson random variable with parameter λ.P [X is even) is

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Test: Probability and Statistics - 5 - Question 16

A teacher on grading an exam finds that the percent marks X have a mean of 62 and a standard deviation of 4. Feeling that the exam may have been unduly difficult, he would like to report a mean of 70 and a standard deviation of 5. He would achieve this by the linear transformation Y = pX + q, where p and q are respectively

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⇒ 70 = 62 p + q

Test: Probability and Statistics - 5 - Question 17

What is the correlation coefficient between x and y for the given data :

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Test: Probability and Statistics - 5 - Question 18

The mean height of 500 students is 151 cm and the standard deviation is 15 cm. Assuming that the heights are normally distributed, find how many student’s height lie between 120 and 155 cms?

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Test: Probability and Statistics - 5 - Question 19

Let X be a binomial random variable with parameters n and p. If the mean and the standard deviation of X are 3 and 3/2, respectively, then what is the value of (n, p)?

Detailed Solution for Test: Probability and Statistics - 5 - Question 19

Standard deviation = 3/2

Test: Probability and Statistics - 5 - Question 20

Suppose that 20 misprints are distributed randomly in a book of 900 pages. Assuming Poisson distribution, the probability that a chapter of 30 pages contains 2 misprints is

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