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Chapter 9: Q2E (page 604)

2. Suppose that a random variable X has the F distribution with three and eight degrees of freedom. Determine the value of c such that Pr(X>c) = 0.975

Short Answer

Expert verified

The required value of c is 0069.

Step by step solution

01

Given Information

A random variable X has an F distribution with three and eight degrees of freedom.

02

Determining the value of c

Given X~F3,8

Let Y= 1/X ~F8,3

thus

P(X > c) = 0.975

P(Y< 1/c) = 0.975

Thus, by using F distribution table

\begin{aligned}c=\frac{1}{F{_{8,3}}^{-1}(0.975)}\end{aligned}

\begin{aligned}=0.069\end{aligned}

Therefore the required value of c is 0.069

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Most popular questions from this chapter

Suppose that X1,鈥�.., Xn forms a random sample from the normal distribution with unknown mean 碌 and unknown variance 蟽2. Classify each of the following hypotheses as either simple or composite:

a) H0 : 碌 = 0 and 蟽=1

b) H0 : 碌 > 3 and 蟽<1

c) H0 : 碌 = -2 and 蟽2<5

d) H0 : 碌 = 0
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