WorksheetsMathematical statistics
Total questions: 23
Worksheet time: 12mins
Standard deviation is the ________ of variance.
Root
Square root
Normal
Variance
The mean is the ________ of a set of values.
Average
Median
Mode
Range
In a normal distribution, approximately ________ of the data falls within one standard deviation of the mean.
99%
50%
95%
68%
The variance is a measure of ________ in a data set.
Central tendency
Dispersion
Correlation
Skewness
Write the probability mass function (PMF) of a Bernoulli distribution.
P(X=x) = p (1-p)^(1-x), x=0,1
P(X=x) = p^x (1-p)^(1-x), x=0,1,.....
P(X=x) = p^x (1-p)^(1-x), x=0,1
P(X=x) = p^x (1-p)(1-x), x=0,1
The coefficient of variation is a measure of ________ relative to the mean.
Dispersion
Central tendency
Skewness
Correlation
In a standard normal distribution, the mean is equal to ________.
1
0
None of the above
2
The median is the ________ value in a sorted data set.
Lowest
Middle
Highest
Average
The mean of a binomial distribution is ________.
np
npq
p-1
pq
The mode is the value that appears ________ in a data set.
Most frequently
Least frequently
In the middle
At the ends
In a Poisson distribution, the mean is equal to the ________.
Mode
Median
Standard deviation
Variance
The interquartile range (IQR) is a measure of ________ in a data set.
Correlation
Skewness
Dispersion
Central tendency
The range is the difference between the ________ and the minimum value in a data set.
Mean
Median
Maximum
Mode
The skewness of a distribution indicates the ________ of the data.
Correlation
Central tendency
Dispersion
Symmetry
The variance of a sample is calculated using ________ in the denominator.
N
2N
N-1
N+1
Formula for a random variable
Var(X)=E[X2]+(E[X])2
Var(X)=E[(X−μ)2]=E[X2]−(E[X])2
Var(X)=E[(X−μ)2]=E[X2]−(E[X])
Var(X)E[(X−μ)2]=E[X2]−(E[X])2
The range of a data set is calculated as the difference between the ________ and the minimum value.
Mean
Maximum
Median
Mode
The standard deviation is a measure of ________ in a data set.
Skewness
Correlation
Dispersion
Central tendency
The probability of success in a binomial distribution is denoted by ________.
r
n
q
p
Characteristic Function (CF)
φX(t)=E[eit]
φX(t)=E[-eitX]
φX(t)=E[eiX]
φX(t)=E[eitX]
The cumulative distribution function (CDF) of a random variable gives the probability that the variable is ________ a certain value.
Less than
Greater than
Equal to
Not equal to
The variance of a population is denoted by ________.
σ
μ
p
σ²
The central limit theorem states that the distribution of the sample mean approaches a ________ distribution as the sample size increases.
Poisson
Binomial
Uniform
Normal
