# Multiple choice questions on F-Distribution( statistical techniques-III) for AKTU Examination

Here In this post we will discuss the important questions of the Sample distribution of statistical techniques-III  . These questions will help you in your mid semesters exams or the semester exams or any other competitive exams. And this will also help in your upcoming  AKTU semester exam.

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1. The mean of the f – distribution is equal to ___________

a) v2 / (v2 – 2) for v2 > 2

b) v2 / (v2 – 2)2 for v2 > 2

c) v2 / (v2 – 2)3 for v2 > 2

d) v2 / (v2 – 2)-1 for v2 > 2

Explanation: The mean of the distribution is equal to v2 / (v2 – 2) for v2 > 2. v2 denotes the degree of freedom of F-Distribution.

2. Variance is equal to [(v1 + v2 – 2)] / [v1 * (v2 – 2)2 * (v2 – 4)] for v2 > 4 for a f-Distribution.

a) True

b) False

Explanation: Variance is equal to [2 * v22 * (v1 + v2 – 2)] / [ v1 * (v2 – 2)2 * (v2 – 4)] for v2 > 4 for a f-Distribution where v1 and v2 denote the degrees of freedom of f-Distribution.

3. Which of the following distributions is Continuous?

a) Binomial Distribution

b) Hyper-geometric Distribution

c) F-Distribution

d) Poisson Distribution

Explanation: Binomial, Poisson and Hyper geometric distributions are Discrete Distributions. Only F- Distribution is Continuous Distribution in the given Distributions.

4. Which of the following distributions is used to compare two variances?

a) T – Distribution

b) F – Distribution

c) Normal Distribution

d) Poisson Distribution

Explanation: F – Distribution is used when we require for comparing two variances. It uses a f-Test to compare two values of variances.

5. F-Distribution cannot take negative values.

a) True

b) False

Explanation: The value of the F-distribution is always positive, or zero. The variances are the square of the deviations and hence cannot assume negative values. Its value lies between 0 and ∞.

6. There is only 1 parameter in F-Distribution.

a) True

b) False

Explanation: There are 2 parameters in F-Distribution v1 and v2. They are called degrees of freedom of F-Distribution.

7. Find the Expectation for a F- Distribution variable with v1 = 7 and v2 = 8.

a) 4/7

b) 4/6

c) 4/3

d) 4/5

Explanation: The Expectation for F-Distribution is given as

E(X) = v2 / (v2 – 2) for v2 > 2

Hence, E(X) = 8 / (8-2)

E(X) = 4/3.

because Expected value is equal to mean.

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