 # Which of the following is(are) True? I. The means of the Student’s t and standard normal distributions are equal. II. The standard normal distribution approaches the Student’s t distribution as the degrees of freedom becomes large. A. I only B. II only C. Both I and II D. Neither I nor II Cabiolab 2020-10-25 Answered
Which of the following is(are) True?
I. The means of the Student’s t and standard normal distributions are equal.
II. The standard normal distribution approaches the Student’s t distribution as the degrees of freedom becomes large.
A. I only
B. II only
C. Both I and II
D. Neither I nor II
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Given information
In the question we are given with the following two statements:
Statement 1: "The means of the Student’s t and standard normal distributions are equal."
Statement 2: "The standard normal distribution approaches the Student’s t distribution as the degrees of freedom becomes large."
and we have to check whether they are true or not.
The probability density function (pdf) of standard normal distribution is:
${f}_{X}\left(x\right)={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\frac{1}{\sqrt{2\pi }}\mathrm{exp}\left\{\frac{-{x}^{2}}{2}\right\}dx$
where X is a random variable following Standard Normal distribution.And, standard normal distribution have mean as 0 and variance as 1.
$X\sim N\left(0,1\right)$
The probability density function of students