Model Test Paper, Mathematical Statistics - 2017 - IIT JAM MCQ

The differential equation 2ydx – (3y – 2x)dy = 0 is

What should be the value of z used in a 93% confidence interval?

Let X be a discrete random variable with values x = 0, 1, 2 and probabilities P(X = 0) = 0.25, P(X = 1) = 0.50, and P(X = 2) = 0.25, respectively.Find E(X²⁾

If two dice are thrown, what is the expected value of sum of the face values?

Let a_n be a sequence such that a₁ = a, a₂ = b and an = (a + a_n–1)/2 for n > 2. Calculate the limit?

  Integration by Parts results in

A function f is defined on interval (0, 1) as follows

then which one of the following is true?

Let f : R → R be s.t. f(x – f(y) ≤ (x – y)² then which of the following is TRUE ?

If two events A and B are such that P(A^c) = 0.3, P(B) = 0.4, P(A ∩ B^c) = 0.5, then P(B/A ∪ B^c) =

 A die is thrown (n + 2) times. After each throw a ‘+’ is recorded for 4, 5 or 6 and ‘–’ for 1, 2 or 3, the signs forming an ordered sequence each, except the first and the last sign, is attached a characteristic random variable which takes the value 1 if both the neighbouring signs differ from the one between them and 0 otherwise. If X₁, X₂, ..., X_n are characteristic random variables, find the mean and variance of

In the regression line Y = a + bX:

What would a chi- square significance value of P > 0.05 suggest?

A random variable X has the density function f(x) = c/(x² + 1). where  –∞ < x < ∞. Find the probability that X² lies between 1/3 and 1.

Y is an exponential random variable with parameter λ = 0.2. Given the event A = {Y < 2}.
Find the conditional expected value, E [Y | A].

An examination paper has 150 multiple- choice questions of one mark each, with each question having four choice. Each incorrect answer fetches- 0.25 mark. Suppose 1000 students choose all their answers randomly with uniform probability. The sum total of the expected marks obtained by all these students is :

If probability density function of a random variable X is

f(x) = x² for –1 < x < 1, and

      = 0 for any other value of x

then, the percentage probability     is

Let F(x, y) be the d.f. of X and Y

if : F(x, y) = 1, for x + 2y ≥ 1

F(x, y) = 0, for x + 2y < 1,
then

If the product moment of X and Y is 3 and the mean of X and Y are both equal to 2, then what is the covariance of the random variables 2X + 10 and – 5/2Y + 3?

If X ~ N(μ,  σ²) and X₁, X₂, ..., X_n be a random sample from the population X, then

Which of the following are true statements?
I. The are under the curve of the t- distribution between ± 1 standard deviation is greater when d.f. = 5 than when d.f. = 10.
II. There is less are in the tails, beyond ± 3 standard deviations, of t-distribution when d.f. = 5 than when d.f. = 10.
III. For a given α, the critical t- value increases as d.f. decreases.

American Airlines claims that the average number of people who pay for in- flight moves, when the plane is fully loaded, is 42 with a standard deviation of 8. A sample of 36 fully loaded planes is taken. What is the probability that fewer than 38 people paid for the in- flight moves?

A symmetric die is thrown 600 times. Find the lower hound for the probability of getting 80 to 120 sixes.

An estimator T₁ = t₁(x₁, x₂, ..., x_n) for q is said to be admissible if for any other estimator T₂ = t₂(x₁, x₂, ..., x_n) for q, the relation is of the type:

A sample of 3 observations, (X₁ = 0.4, X₂ = 0.7, X₃ = 0.9) is collected from a continuous distribution with density

Estimate θ by the method of moments;

In a test of H₀ : μ = 100 against H_A : μ  ≠  100, a sample of size 10 produces a sample mean of 103 and a p- value of 0.08. Thus, at the 0.05 level of significance:

Suppose n = 100. Then the probability of type II error is :