Probability (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 33 - 38 of 72

Get 1 year subscription: Access detailed explanations (illustrated with images and videos) to 165 questions. Access all new questions we will add tracking exam-pattern and syllabus changes. View Sample Explanation or View Features.

Rs. 550.00 or

Question number: 33

» Probability » Distribution Function » Standard Probability Distributions

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Let Y 1 denote the first order statistic in a random sample of size n from a distribution that has the pdf

Equation

Obtain the distribution of Z n =n (Y 1 -θ).

Explanation

To find the distribution of order statistic, the pdf is

Equation

Here denote the first order statistic that is

Equation

The cdf of x is

Equation

Equation

The pdf of Y 1 is

Equation

Equation

Equation

Then, the distribution of Z n =n (Y 1 -θ) is

Equation

Equation

Equation

… (10 more words) …

Question number: 34

» Probability » Distribution Function » Standard Probability Distributions

Appeared in Year: 2013

Essay Question▾

Describe in Detail

Find the distribution of the ratio of two iid random variables with density function:

Equation

Explanation

Let consider x and y are two iid random variable with density function is same. Then find the distribution of their ratio that is x/y. The joint pdf of x and y is

Equation

To find this we use Jacobian transformation technique, assume

X/Y = u, Y = v

X

… (54 more words) …

Question number: 35

» Probability » Standard Probability Distributions » Normal

Appeared in Year: 2012

Essay Question▾

Describe in Detail

12.3 % of the candidates in a public examination score at least 70%, while another 6.3 % score at most 30%. Assuming the underlying distribution to be normal, estimate the percentage of candidates scoring 80 % or more.

Explanation

Let total marks obtain is 100. Assuming the underlying distribution to be normal, the mean µ and variance σ 2. It is given that

Equation

The value of z corresponding to an area

0.500 - 0.123 = 0.377

We can write

Equation

Equation

Similarly, . It is given that

… (50 more words) …

Question number: 36

» Probability » Probability of M Events Out of N

Appeared in Year: 2013

Essay Question▾

Describe in Detail

A fair die is rolled twice. Let A be the event that the first throw shows a number ≤ 2, and B be the event that the second throw shows at least 5. Show that P (AUB) =5/9.

Explanation

A fair die is rolled twice, the sample space consists of thirty six outcomes. The sample space is

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

(3, 1), (3, 2), (3, 3), (3, 4),

… (160 more words) …

Question number: 37

» Probability » Probability of M Events Out of N

Appeared in Year: 2014

Essay Question▾

Describe in Detail

A positive integer X is selected at random from the first 50 natural numbers.

Calculate P (X + 96/X > 50).

Explanation

Total number of possible outcomes = number of ways in which the one random number can be chosen out of 50

Equation

Let Y be the event whose satisfied the relation, X + 96/X > 50

For which X we choose is

Equation

Equation

Equation

Equation

So, X takes values

… (38 more words) …

Question number: 38

» Probability » Elements of Measure Theory

Appeared in Year: 2014

Essay Question▾

Describe in Detail

Suppose that all the four outcomes 0 1, 0 2, 0 3 and 0 4 of an experiment are equally likely. Define A = (0 1, 0 4), B = (0 2, 0 4) and C = (0 3, 0 4). What can you say about the pairwise independence and mutually independence of the events A, B and C?

Explanation

Given that there are four outcomes. Define A = (O 1, O 4), B = (O 2, O 4), C = (O 3, O 4)

Their intersection is Equation and Union is AUBUC = (O 1, O 2, O 3, O

… (114 more words) …

f Page
Sign In