### Give description of probability distribution function

Assignment Help Mathematics
##### Reference no: EM13119359

Description of Probability distribution function

Please give step-by-step process for solving the following probability problems.

Let X ~ Exp(lamda1) and that Y ~ Exp(lambda2).
Further assume that X and Y are independent.

(a) Write down the joint pdf (probability distribution function) of X and Y, fXY(x,y).
(b) For t > 0, prove that P(Y < tX) = t lambda2 / ( lambda1 + t lambda2).
(c) For simplicity, assume that lambda1 = lambda2 = 1, and let T = Y/X. Use part (b) to find the pdf (probability distribution function) of T, fT(t).

#### Questions Cloud

 Solving quadratic equations by completing square : An interesting method for solving quadratic equations came from India. The steps are-Move the constant term to the right side of the equation. Multiply each term in the equation by four times the coefficient of the x2 term. What is the molar mass of the compound : An unknown gas effuses at a rate of 86.6 mol/hr. Under similar conditions, I2 effuses at a rate of 30.4 mol/hr. What is the molar mass of the compound. Find confidence interval for the population difference : Historical data suggests a standard deviation in the first sample of 10 and a standard deviation in the second sample of 16. Find a 95% confidence interval for the population difference. Give description of probability distribution function : Description of Probability distribution function, Please give step-by-step process for solving the following probability problems. What is the partial pressure of the gas produced : If the measured gas pressure in a collection flask during a gas-forming reaction was determined to be 1.44 atm, and the atmospheric pressure that day was measured as 0.95 atm. What functional difference between ventricular hypertrophy : What is the functional difference between ventricular hypertrophy due to exercise and hypertrophy due to congestive heart failure? Is there evidence that the cost of attendance has increased : The sample mean was \$22,098 and the standard deviation was \$6050. Is there evidence at the 1% significance level that the cost of attendance has increased? Type of damage occur after grabbing a door frame : What type of damage could occur if you grabbed a door frame with your left arm stepped with your right leg the leg shoots out from under you and you bounce down hitting the edge.

### Write a Review

#### Determine the triple integral

Find the multiple integral under given condition using cylindrical coordinate - Determine the triple integral

#### Least square regression equation

If the train were announced to be running  thirteen minutes late, how many times would you predict the man next to you would check the time?

#### The sequence of late times

The sequence of late times

Chi square test

#### Calculate the change in the odds of chd

Calculate the change in the odds of CHD in males for each additional time they exercise on average each week.

#### Chart of the topological manifold

De?nition of smoothness of functions on a smooth manifold is chart independent and hence geometric.

#### Why is the test you select the most appropriate

Blood pressure measurements are taken on a set of patients before & after they receive a lumbar puncture [spinal tap]. You are interested in determining if there is a difference between mean arterial blood pressure between the pre & post measures. Wh..

#### Compute the mean and variance for binomial distribution

Compute the mean and variance for binomial distribution. Calculate the mean and standard deviation (by hand) for the binomial distribution with the probability of a success being 1/4, 1/2, 3/4.

#### Solving problems conditional probability

Solving problems conditional probability

#### Determine the equation of the straight line

Determine the equation of the straight line and Write a linear equation that describes the book value of the machine each year

#### Find the expected value- lottery

Assuming that there is no cost to enter the .sweepstakes, find the expected value of the amount won for one entry. Round to the nearest tenth.

#### Determine the probability that the spinner lands on

Assume that the spinner cannot land on a line. Determine the probability that the spinner lands on (a) red, (b) green, (c) yellow, (d) green. The spinner is divided into 8 halves. There are (a) red = 4, (b) green = 1, (c) yellow = 1, and (d) blue = ..