Let the random variable X denote the time (hours) for which a part is waiting for...

Let the random variable X denote the time (hours) for which a part is waiting for the beginning of the inspection process since its arrival at the inspection station, and let Y denote the time (hours) until the inspection process is completed since its arrival at the inspection station. Since both X and Y measure the time since the arrival of the part at the inspection station, always X < Y is true. The joint probability density function for X and Y is given as follows:

???(?,?) = ??−?−??, where ? < ? < ? < ∞.
1.) What is the Value of k?

2.) What is the covariance of (X,Y)?

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

The random variable X milliseconds is the total access time (waiting time + reading time) to...

The random variable X milliseconds is the total access time (waiting time + reading time) to obtain a block of information from a computer disk. X is evenly distributed between 0 and 12 milliseconds. Before making a determined task, the computer must access 12 different information blocks from the disk. (The access times for different blocks are independent one of the other.) The total access time for all information is a random variable A milliseconds. (1) What is the E...

Two dice are rolled. Let the random variable X denote the number that falls uppermost on...

Two dice are rolled. Let the random variable X denote the number that falls uppermost on the first die and let Y denote the number that falls uppermost on the second die. (a) Find the probability distributions of X and Y. x 1 2 3 4 5 6 P(X = x) y 1 2 3 4 5 6 P(Y = y) (b) Find the probability distribution of X + Y. x + y 2 3 4 5 6 7 P(X...

An unbiased coin is tossed four times. Let the random variable X denote the greatest number...

An unbiased coin is tossed four times. Let the random variable X denote the greatest number of successive heads occurring in the four tosses (e.g. if HTHH occurs, then X = 2, but if TTHT occurs, then X = 1). Derive E(X) and Var(X). (ii) The random variable Y is the number of heads occurring in the four tosses. Find Cov(X,Y).

Let X denote a random variable that follows a binomial distribution with parameters n=5, p=0.3

Let X denote a random variable that follows a binomial distribution with parameters n=5, p=0.3, and Y denote a random variable that has a Poisson distribution with parameter λ = 6. Additionally, assume that X and Y are independent random variables. (a) What are the possible values for (X, Y ) pairs. (b) Derive the joint probability distribution function for X and Y. Make sure to explain your steps. (c) Using the joint pdf function of X and Y, form...

Let X denote a random variable that follows a binomial distribution with parameters n=5, p=0.3, and...

Let X denote a random variable that follows a binomial distribution with parameters n=5, p=0.3, and Y denote a random variable that has a Poisson distribution with parameter λ = 6. Additionally, assume that X and Y are independent random variables. What are the possible values for (X, Y ) pairs. Derive the joint probability distribution function for X and Y. Make sure to explain your steps. Using the joint pdf function of X and Y, form the summation /integration...

Let X denote a random variable that follows a binomial distribution with parameters n=5, p=0.3, and...

Let X denote a random variable that follows a binomial distribution with parameters n=5, p=0.3, and Y denote a random variable that has a Poisson distribution with parameter λ = 6. Additionally, assume that X and Y are independent random variables. What are the possible values for (X, Y ) pairs. Derive the joint probability distribution function for X and Y. Make sure to explain your steps. Using the joint pdf function of X and Y, form the summation /integration...

Let 'x' be a random variable that represents the length of time it takes a student...

Let 'x' be a random variable that represents the length of time it takes a student to write a term paper for Dr. Adam's Sociology class. After interviewing many students, it was found that 'x' has an approximately normal distribution with a mean of µ = 7.3 hours and standard deviation of ơ = 0.8 hours. For parts a, b, c, Convert each of the following x intervals to standardized z intervals. a.) x < 8.1 z < b.) x...

Let z denote a random variable having a normal distribution with ? = 0 and ?...

Let z denote a random variable having a normal distribution with ? = 0 and ? = 1. Determine each of the probabilities below. (Round all answers to four decimal places.) (a) P(z < 0.3) = (b) P(z < -0.3) = (c) P(0.40 < z < 0.85) = (d) P(-0.85 < z < -0.40) = (e) P(-0.40 < z < 0.85) = (f) P(z > -1.26) = (g) P(z < -1.5 or z > 2.50) =

Let the continuous random variable D denote the diameter of the hole drilled in an aluminum...

Let the continuous random variable D denote the diameter of the hole drilled in an aluminum sheet. The target diameter to be achieved is 12.5mm. Random disturbances in the process often result in inaccuracy. Historical data shows that the distribution of D can be modelled by the PDF, f(d) = 20e−20(d−12.5), d ≥ 12.5. If a part with diameter > 12.6 mm needs to be scrapped, what is the proportion of those parts? What is the CDF when the diameter...

Let T be a Kumaraswamy random variable, and X be a Weibull random variable, the T-X...

Let T be a Kumaraswamy random variable, and X be a Weibull random variable, the T-X family will be called the Kumaraswamy-Weibull distribution. Using W[F(x)]=F(x). Obtain (a) both the cdf and pdf of the Kumaraswamy-Weibull distribution. (b) both the hazard and reverse hazard function Kumaraswamy-Weibull distribution. (c) the quantile function Kumaraswamy-Weibull distribution.

Subjects