1.
For a continuous random variable, P(X= x ) = 1
Correct Answer
B. False
Explanation
False : For a continuous random variable, probability at any particular point is 0
2.
Number of goals in a football match is an example of continuous random variable.
Correct Answer
B. False
Explanation
it is a discrete random variable
3.
Mean and variance is always same for Exponential distribution.
Correct Answer
B. False
Explanation
mean =1/m and variance = 1/m^2
4.
Standard normal distribution is also known as Rectangular distribution.
Correct Answer
B. False
Explanation
Continuous Uniform distribution is known as Rectangular distribution
5.
Critical region is known as Acceptance region.
Correct Answer
B. False
Explanation
it is known as Rejection region
6.
For a continuous random variable, P(X≥ a)=P(X > a) for all a.
Correct Answer
A. True
Explanation
for a continuous r.v. P(X=a)=0
7.
For Rectangular distribution, mean=standard deviation.
Correct Answer
B. False
Explanation
true for Exponential Distribution
8.
The burden of justification is always on the Null hypothesis
Correct Answer
B. False
Explanation
it is on the Alternative hypothesis
9.
Variance of sampling distribution is called as Standard Error.
Correct Answer
B. False
Explanation
standard deviation of sampling distribution is called standard error.
10.
Number of pages in a book is an example of continuous random variable
Correct Answer
B. False
Explanation
Discrete random variable
11.
Parameters of Standard normal distribution are : mean=1 and variance = 0
Correct Answer
B. False
Explanation
mean=0, variance = 1
12.
The region where we accept alternative hypothesis is known as Acceptance region
Correct Answer
B. False
Explanation
the region where we accept Null hypothesis is known as Acceptance region.
13.
Sample mean is a unbiased estimator of Population mean
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.
14.
The Volume of Milk in a glass is an example of continuous random variable
Correct Answer
A. True
Explanation
volume can take any real number in a particular range.
15.
Sample median is an example of statistic.
Correct Answer
A. True
Explanation
sample median is a function of sample observation and therefore it is an example of statistic
16.
For any continuous random variable X, P(a < X < b ) < P( a ≤ X ≤ b)
Correct Answer
B. False
Explanation
for a continuous r.v. P(X=a)=0
17.
Following is a probability distribution function of a continuous random variable, X
f(x)= x 0 < x < 1
Correct Answer
B. False
Explanation
show that total integration is 1
18.
Temperature in Mumbai is an example of continuous random variable.
Correct Answer
A. True
Explanation
temperature can take any real value in a particular range.
19.
Number of corona positive cases in Mumbai is an example of Continuous r.v.
Correct Answer
B. False
Explanation
Discrete r.v.
20.
Death rate due to corono virus is an example of continuous r.v.
Correct Answer
A. True
Explanation
yes it can take any real number value.
21.
We can obtain Median of a continuous distribution using the condition : f(x) =1/2
Correct Answer
B. False
Explanation
condition : F(x)=1/2 not pdf f(x)=1/2
22.
Forgetfulness ( lack of Memory) is the property associated with Rectangular distribution.
Correct Answer
B. False
Explanation
with Exponential distribution
23.
Bias = E(estimator)-parameter
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.
24.
Power of test = 1 – P(Type I error )
Correct Answer
B. False
Explanation
Power of test = 1 – P(Type II error )
25.
With usual notations, f’(x)=F(x).
Correct Answer
B. False
Explanation
With usual notations, f(x)=F'(x).
26.
P(Type 1 error) = P ( Reject Ho / Ho is true)
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).
27.
F(x)= 1/ (a-b) if a < x < b
Correct Answer
B. False
Explanation
f(x)= 1/ (b-a) if a < x < b see the range of x
28.
If X~ N(mean=5, Variance = 4) then 2X~N(10, 8)
Correct Answer
B. False
Explanation
2X~N(10, 16)
29.
Parameter is a function of population values
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.
30.
Statistic is a branch of mathematics with deals with uncertain events.
Correct Answer
B. False
Explanation
Statistic (without 's') is a function of sample values