Fybsc Paper 2 Sem 2 Practice Test

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| By Sanjay.karande88

Sanjay.karande88

Community Contributor

Quizzes Created: 1 | Total Attempts: 37

Questions: 30 | Attempts: 37 | Updated: Apr 19, 2023

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Questions and Answers

1.

For a continuous random variable, P(X= x ) = 1
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

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

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2.

Number of goals in a football match is an example of continuous random variable.
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
it is a discrete random variable

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3.

Mean and variance is always same for Exponential distribution.
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

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

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4.

Standard normal distribution is also known as Rectangular distribution.
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
Continuous Uniform distribution is known as Rectangular distribution

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5.

Critical region is known as Acceptance region.
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
it is known as Rejection region

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6.

For a continuous random variable, P(X≥ a)=P(X > a) for all a.
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

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

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7.

For Rectangular distribution, mean=standard deviation.
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
true for Exponential Distribution

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8.

The burden of justification is always on the Null hypothesis
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
it is on the Alternative hypothesis

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9.

Variance of sampling distribution is called as Standard Error.
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
standard deviation of sampling distribution is called standard error.

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10.

Number of pages in a book is an example of continuous random variable
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
Discrete random variable

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11.

Parameters of Standard normal distribution are : mean=1 and variance = 0
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
mean=0, variance = 1

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12.

The region where we accept alternative hypothesis is known as Acceptance region
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

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

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13.

Sample mean is a unbiased estimator of Population mean
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

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.

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14.

The Volume of Milk in a glass is an example of continuous random variable
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

Explanation
volume can take any real number in a particular range.

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15.

Sample median is an example of statistic.
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

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

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16.

For any continuous random variable X, P(a < X < b ) < P( a ≤ X ≤ b)
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

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

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17.

Following is a probability distribution function of a continuous random variable, X f(x)= x 0 < x < 1
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
show that total integration is 1

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18.

Temperature in Mumbai is an example of continuous random variable.
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

Explanation
temperature can take any real value in a particular range.

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19.

Number of corona positive cases in Mumbai is an example of Continuous r.v.
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
Discrete r.v.

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20.

Death rate due to corono virus is an example of continuous r.v.
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

Explanation
yes it can take any real number value.

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21.

We can obtain Median of a continuous distribution using the condition : f(x) =1/2
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

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

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22.

Forgetfulness ( lack of Memory) is the property associated with Rectangular distribution.
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
with Exponential distribution

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23.

Bias = E(estimator)-parameter
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

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.

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24.

Power of test = 1 – P(Type I error )
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
Power of test = 1 – P(Type II error )

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25.

With usual notations, f’(x)=F(x).
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

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

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26.

P(Type 1 error) = P ( Reject Ho / Ho is true)
- A.
  
  True
- B.
  
  False
Correct Answer
A. 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).

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27.

F(x)= 1/ (a-b) if a < x < b
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

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

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28.

If X~ N(mean=5, Variance = 4) then 2X~N(10, 8)
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
2X~N(10, 16)

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29.

Parameter is a function of population values
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

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.

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30.

Statistic is a branch of mathematics with deals with uncertain events.
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
Statistic (without 's') is a function of sample values

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Current Version
Apr 19, 2023

Quiz Edited by
ProProfs Editorial Team
Mar 28, 2020

Quiz Created by
Sanjay.karande88

Fybsc Paper 2 Sem 2 Practice Test

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

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

Mean and variance is always same for Exponential distribution.

Standard normal distribution is also known as Rectangular distribution.

Critical region is known as Acceptance region.

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

For Rectangular distribution, mean=standard deviation.

The burden of justification is always on the Null hypothesis

Variance of sampling distribution is called as Standard Error.

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

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

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

Sample mean is a unbiased estimator of Population mean

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

Sample median is an example of statistic.

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

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

Temperature in Mumbai is an example of continuous random variable.

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

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

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

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

Bias = E(estimator)-parameter

Power of test = 1 – P(Type I error )

With usual notations, f’(x)=F(x).

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

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

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

Parameter is a function of population values

Statistic is a branch of mathematics with deals with uncertain events.