Solution Found!
. Suppose that X has the t distribution with m degrees of
Chapter 8, Problem 1(choose chapter or problem)
. Suppose that X has the t distribution with m degrees of freedom (m > 2). Show that Var(X) = m/(m 2). Hint: To evaluate E(X2), restrict the integral to the positive half of the real line and change the variable from x to y = x2 m 1 + x2 m . Compare the integral with the p.d.f. of a beta distribution. Alternatively, use Exercise 21 in Sec. 5.7
Questions & Answers
QUESTION:
. Suppose that X has the t distribution with m degrees of freedom (m > 2). Show that Var(X) = m/(m 2). Hint: To evaluate E(X2), restrict the integral to the positive half of the real line and change the variable from x to y = x2 m 1 + x2 m . Compare the integral with the p.d.f. of a beta distribution. Alternatively, use Exercise 21 in Sec. 5.7
ANSWER:Step 1 of 5
Let Y and Z be two independent random variables from distribution with degrees of freedom and from the standard normal distribution, respectively. Random variable defined as
is said to have distribution with degrees of freedom.