Question: Show that if the random variable X has uniform distribution over the interval (0,1), the random variable - 2 log X has a chi-square distribution

Show that if the random variable X has uniform distribution over the interval (0,1), the random variable - 2 log X has a chi-square distribution with 2 degrees of freedom.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

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

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Statistics For Engineers And Scientists Questions!

100,000 randomly selected adults were asked whether they drink at least 48 oz of water each day and only 45% said yes. Identify the sample and population. 12 The manager of a car dealership records...

In this exercise, we construct an example of a sequence of random variables Zn such that but That is, Zn converges in probability to 0, but Zn does not converge to 0 with probability 1. Indeed, Zn...

Suppose that X1, . . . , Xn form a random sample from the uniform distribution on the interval [0, 1], and let W denote the range of the sample, as defined in Example 3.9.7. Also, let gn(x) denote...

solve these practice problems The relative conductivity of a semiconductor device is determined by the amount of impurity "doped" into the device during its manufacture. A silicon diode to be used...

Question 12 (1 point) On average, each insurance claim forwarded to a certain division of an insurance company has a 40% chance of getting approved after the preliminary review. In addition to that,...

If p has a uniform distribution in the range (0, 1) show that -2 log, p has ax-distribution with degrees of freedom 2. If there are k independent tests, each with a p-value, then A = -2 log p, has a...

may I get help please? 7. Suppose a random sample of size n = 12 is taken from the uniform distribution on the interval [0, 1]. The variance for the uniform distribution is 1/12. Let X denote the...

Characteristic functions of probability matter 1. Find the characteristic function of a random variable: a) with uniform distribution in the interval ( l , l ) b) with density given by p ( x ) = ( 1...

a). Calculate the star-height of the rational expression R = ((a*b)* ba*)* . b). What is the star height of L( R)? c). Describe L( R). d). What is the extended star height of R? e). Write a star-free...

Explain the trade-offs among selecting between the types of conversion in Questions 3, 4, and 5.

Ashok and Neena have accumulated over $ 4 . 8 million during their 5 0 years of marriage. They have two children and six grandchildren. How much money can they gift to their children in 2 0 2 3...

a. The United States Congress is well qualified to debate and set generally accepted accounting principles. Comment. b. Speculate on why these bills were directed to amend the Securities Exchange Act...