Fybsc Paper 2 Sem 2 Practice Test

1. Number of pages in a book is an example of continuous random variable

True

False

Discrete random variable

Explanation

Discrete random variable

2. Number of goals in a football match is an example of continuous random variable.

True

False

it is a discrete random variable

Explanation

it is a discrete random variable

3. For a continuous random variable, P(X≥ a)=P(X > a) for all a.

True

False

for a continuous r.v. P(X=a)=0

Explanation

for a continuous r.v. P(X=a)=0

4. For Rectangular distribution, mean=standard deviation.

True

False

true for Exponential Distribution

Explanation

true for Exponential Distribution

5. Parameters of Standard normal distribution are : mean=1 and variance = 0

True

False

mean=0, variance = 1

Explanation

mean=0, variance = 1

6. The region where we accept alternative hypothesis is known as Acceptance region

True

False

the region where we accept Null hypothesis is known as Acceptance region.

Explanation

the region where we accept Null hypothesis is known as Acceptance region.

7. Following is a probability distribution function of a continuous random variable, X f(x)= x 0 < x < 1

True

False

show that total integration is 1

Explanation

show that total integration is 1

8. Critical region is known as Acceptance region.

True

False

it is known as Rejection region

Explanation

it is known as Rejection region

9. We can obtain Median of a continuous distribution using the condition : f(x) =1/2

True

False

condition : F(x)=1/2 not pdf f(x)=1/2

Explanation

condition : F(x)=1/2 not pdf f(x)=1/2

10. Forgetfulness ( lack of Memory) is the property associated with Rectangular distribution.

True

False

with Exponential distribution

Explanation

with Exponential distribution

11. Temperature in Mumbai is an example of continuous random variable.

True

False

temperature can take any real value in a particular range.

Explanation

temperature can take any real value in a particular range.

12. Parameter is a function of population values

True

False

This statement is true because a parameter is a numerical summary of a population, and it is typically calculated using population values. A parameter represents a characteristic of the entire population, such as the mean or standard deviation. In contrast, a statistic is a numerical summary of a sample, which represents only a subset of the population. Therefore, a parameter is indeed a function of population values.

Explanation

This statement is true because a parameter is a numerical summary of a population, and it is typically calculated using population values. A parameter represents a characteristic of the entire population, such as the mean or standard deviation. In contrast, a statistic is a numerical summary of a sample, which represents only a subset of the population. Therefore, a parameter is indeed a function of population values.

13. P(Type 1 error) = P ( Reject Ho / Ho is true)

True

False

The statement is true because a Type 1 error occurs when the null hypothesis (Ho) is true, but it is rejected based on the sample data. In other words, it is the probability of incorrectly rejecting a true null hypothesis. Therefore, the probability of Type 1 error is indeed P(Reject Ho / Ho is true).

Explanation

The statement is true because a Type 1 error occurs when the null hypothesis (Ho) is true, but it is rejected based on the sample data. In other words, it is the probability of incorrectly rejecting a true null hypothesis. Therefore, the probability of Type 1 error is indeed P(Reject Ho / Ho is true).

14. The Volume of Milk in a glass is an example of continuous random variable

True

False

volume can take any real number in a particular range.

Explanation

volume can take any real number in a particular range.

15. Sample median is an example of statistic.

True

False

sample median is a function of sample observation and therefore it is an example of statistic

Explanation

sample median is a function of sample observation and therefore it is an example of statistic

16. The burden of justification is always on the Null hypothesis

True

False

it is on the Alternative hypothesis

Explanation

it is on the Alternative hypothesis

17. Power of test = 1 – P(Type I error )

True

False

Power of test = 1 – P(Type II error )

Explanation

Power of test = 1 – P(Type II error )

18. F(x)= 1/ (a-b) if a < x < b

True

False

f(x)= 1/ (b-a) if a < x < b see the range of x

Explanation

f(x)= 1/ (b-a) if a < x < b see the range of x

19. If X~ N(mean=5, Variance = 4) then 2X~N(10, 8)

True

False

2X~N(10, 16)

Explanation

2X~N(10, 16)

20. For a continuous random variable, P(X= x ) = 1

True

False

False : For a continuous random variable, probability at any particular point is 0

Explanation

False : For a continuous random variable, probability at any particular point is 0

21. Variance of sampling distribution is called as Standard Error.

True

False

standard deviation of sampling distribution is called standard error.

Explanation

standard deviation of sampling distribution is called standard error.

22. With usual notations, f'(x)=F(x).

True

False

With usual notations, f(x)=F'(x).

Explanation

With usual notations, f(x)=F'(x).

23. For any continuous random variable X, P(a < X < b ) < P( a ≤ X ≤ b)

True

False

for a continuous r.v. P(X=a)=0

Explanation

for a continuous r.v. P(X=a)=0

24. Number of corona positive cases in Mumbai is an example of Continuous r.v.

True

False

Discrete r.v.

Explanation

Discrete r.v.

25. Mean and variance is always same for Exponential distribution.

True

False

mean =1/m and variance = 1/m^2

Explanation

mean =1/m and variance = 1/m^2

26. Bias = E(estimator)-parameter

True

False

The statement "Bias = E(estimator)-parameter" is true. Bias refers to the difference between the expected value of an estimator and the true parameter being estimated. It measures the systematic error in the estimation process. Therefore, the given statement accurately represents the concept of bias.

Explanation

The statement "Bias = E(estimator)-parameter" is true. Bias refers to the difference between the expected value of an estimator and the true parameter being estimated. It measures the systematic error in the estimation process. Therefore, the given statement accurately represents the concept of bias.

27. Sample mean is a unbiased estimator of Population mean

True

False

The statement is true because the sample mean is calculated by taking the average of a random sample from a population. Since the sample is random, it is expected to be representative of the population. Therefore, the sample mean provides an unbiased estimate of the population mean, meaning that on average, it will be equal to the true population mean.

Explanation

The statement is true because the sample mean is calculated by taking the average of a random sample from a population. Since the sample is random, it is expected to be representative of the population. Therefore, the sample mean provides an unbiased estimate of the population mean, meaning that on average, it will be equal to the true population mean.

28. Death rate due to corono virus is an example of continuous r.v.

True

False

yes it can take any real number value.

Explanation

yes it can take any real number value.

29. Standard normal distribution is also known as Rectangular distribution.

True

False

Continuous Uniform distribution is known as Rectangular distribution

Explanation

Continuous Uniform distribution is known as Rectangular distribution