Data Science

Probability and Statistics

Question 1
Marks : +2 | -2
Pass Ratio : 10%
Which of the following of a random variable is a measure of spread?
variance
standard deviation
empirical mean
all of the mentioned
Explanation:
Densities with a higher variance are more spread out than densities with a lower variance.
Question 2
Marks : +2 | -2
Pass Ratio : 10%
Which of the following inequality is useful for interpreting variances?
Chebyshev
Stautaory
Testory
All of the mentioned
Explanation:
Chebyshev’s inequality is also spelled as Tchebysheff’s inequality.
Question 3
Marks : +2 | -2
Pass Ratio : 10%
The square root of the variance is called the ________ deviation.
empirical
mean
continuous
standard
Explanation:
Standard Deviation (SD) is the measure of spread of the numbers in a set of data from its mean value.
Question 4
Marks : +2 | -2
Pass Ratio : 10%
Cumulative distribution functions are used to specify the distribution of multivariate random variables.
True
False
Explanation:
In the case of a continuous distribution, it gives the area under the probability density function from minus infinity to x.
Question 5
Marks : +2 | -2
Pass Ratio : 10%
Point out the correct statement.
Some cumulative distribution function F is non-decreasing and right-continuous
Every cumulative distribution function F is decreasing and right-continuous
Every cumulative distribution function F is increasing and left-continuous
None of the mentioned
Explanation:
Every cumulative distribution function F is non-decreasing and right-continuous.
Question 6
Marks : +2 | -2
Pass Ratio : 30%
Chebyshev’s inequality states that the probability of a “Six Sigma” event is less than ___________
10%
20%
30%
3%
Explanation:
If a bell curve is assumed, the probability of a “six sigma” event is on the order of one ten millionth of a percent.
Question 7
Marks : +2 | -2
Pass Ratio : 10%
The expected value or _______ of a random variable is the center of its distribution.
mode
median
mean
bayesian inference
Explanation:
A probability model connects the data to the population using assumptions.
Question 8
Marks : +2 | -2
Pass Ratio : 10%
For continuous random variables, the CDF is the derivative of the PDF.
True
False
Explanation:
For continuous random variables, the PDF is the derivative of the CDF.
Question 9
Marks : +2 | -2
Pass Ratio : 10%
Which of the following random variables are the default model for random samples?
iid
id
pmd
all of the mentioned
Explanation:
Random variables are said to be iid if they are independent and identically distributed.
Question 10
Marks : +2 | -2
Pass Ratio : 10%
Point out the wrong statement.
A percentile is simply a quantile with expressed as a percent
There are two types of random variable
R cannot approximate quantiles for you for common distributions
None of the mentioned
Explanation:
R can approximate quantiles for you for common distributions.