Question: Suppose that a random variable X has the F distribution with m and n degrees of freedom (n > 2). Show that E(X) = n/(n

Suppose that a random variable X has the F with m and n degrees of freedom (n > 2). Show that E(X) = n/(n − 2). Find the value of E(1/Z), where Z has the χ2 with n degrees of freedom.

Step by Step Solution

★★★★★

3.40 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Suppose that X is represented as in Eq 971 Since Y and Z are ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

602-M-S-H-T (3900).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

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.

Suppose that a random variable X has a normal distribution, and for every x, the conditional distribution of another random variable Y given that X = x is a normal distribution with mean ax + b and...

Suppose that a random variable x is assumed to be normally distributed with (unknown) mean m and variance 2 so that its probability density function is The probability (likelihood) of a sequence of...

Suppose that a random variable X has the F distribution with m and n degrees of freedom. Show that the random variable mX/(mX + n) has the beta distribution with parameters = m/2 and = n/2.

3) Let the random variable F have an F distribution with m and n degrees of freedom respectively, that is F~F(m,n). Prove the following: (20 points) m a) Y = 1+ has a beta distribution with...

I will vote your Answer The null hypothesis to be tested is that the K population means are equal-that is, HO:M1 = M2 = ... = MK We make the following additional assumptions: V13 1. The population...

The null hypothesis to be tested is that the K population means are equal-that is, V13 HO:M1 = M2 = ... = MK We make the following additional assumptions: 1. The population variances are equal. 2....

Suppose that the random variable X has an exponential distribution with parameter ? > 0. (i) What are the probability density function, fX(x), and the probability distribution function, FX(x), for...

Help me obtain solutions Suppose that the random variable X follows an exponential distribution with probability density function f(x=20-", ocx 0). Define a new random variable V = X 3 (i) (a) Show...

4. (Statistics Review) (a) Suppose a random variable x follow a normal distribution of N[1,2]. Let := 9x2 - 12. +4, compute : = E(). (Hint: ?,? + 2ab + b2 = (ax + b)2 and use the property of the...

Help with thorough explanations of nm values, thanks! 11. Use the Bohr model for atomic structure and the Balmer-Rydberg equation to answer this question. The Balmer series for hydrogen (see above)...

The flash point of an engine oil is 363F. What is the absolute flash-point temperature in K and R?

Your male patient complaint of discomfort while inflating the balloon doing insertion of indwelling hearing capture what would be the most appropriate action

29. Natashas Flowers, a local florist, purchases fresh flowers each day at the local flower market. The buyer has a budget of $1000 per day to spend. Different flowers have different profit margins,...

To determine how well existing chemical analyses can detect lead in test specimens in water, a civil engineer submits specimens spiked with known concentrations of lead to a laboratory. The chemists...

With reference to Exercise 11.69, find the proportion of variance in the amount of NOx explained by the amount of additive. Data From Exercise 11.69 11.69 A chemical engineer found that by adding...

With reference to Exercise 11.69, find the 95% limits of prediction when the amount of additive is 4.5. Data From Exercise 11.69 11.69 A chemical engineer found that by adding different amounts of an...

The last four years of returns for a stock are as follows: a. What is the average annual return? b. What is the variance of the stock's returns? c. What is the standard deviation of the stock's...

Suppose that you are considering investing in two stocks A and B. After analyzing the two stocks you think that there are three possible states for the economy over the next year. The economic states...

Grotesque Corporation is a public company, and Corporation Fund is a relatively well-diversified mutual fund. The following two graphs show regressions for the market's historic realized returns...