Multiple Choice
Which of the following correctly states the two requirements for a discrete probability distribution?
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4. Probability
Basic Concepts of Probability
Multiple Choice
Which of the following is a property of the -distribution?
A
It is defined only for positive values.
B
Its mean is always greater than .
C
It has heavier tails than the standard normal distribution.
D
It is symmetric about .
Verified step by step guidance1
Recall the definition of the Student's t-distribution: it is a probability distribution that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown.
Understand the shape and properties of the t-distribution: it is symmetric about zero, similar to the standard normal distribution, but with heavier tails.
Recognize that 'heavier tails' means the t-distribution has more probability in the tails compared to the normal distribution, which accounts for greater variability in small samples.
Note that the t-distribution is defined for all real numbers, not just positive values, so it is not limited to positive values only.
Remember that the mean of the t-distribution is zero (when degrees of freedom are greater than 1), so it is not always greater than zero.
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