A computer network behaves like a processor and a memory card. The lifetimes of these components...
A computer network behaves like a processor and a memory card. The lifetimes of these components before failure can be modeled, for constants α> 0 and β> 0, by means of two independent random variables X and Y and exponential laws X ∼ exp (α) and Y ∼ exp (β ).
a) Calculate P (X <Y) and P (Y <X).
b) Calculate the laws of the random variables M = min (X, Y), and show that they are independent.
M = min(X, Y ), R = |X − Y |
Homework Answers
Add Answer to:
A computer network behaves like a processor and a memory card.
The lifetimes of these components...
A device runs until either of two components fails, at which time the device stops running. The j...
A device runs until either of two components fails, at which time the device stops running. The joint probability density function of the lifetimes of the two components, both measured in hours, is given by Ш for 0 < z < 3 and 0SyS3, xy(,y)27 0 otherwise. (a) 6 points Find the marginal probability density function for the random variable X. (b) [8 points] Are X and Y independent random variables? Justify your answer. (c) 6 points] Calculate the probability...
need help for a and c. Thank you! Two components of a laptop computer have the...
need help for a and c. Thank you!
Two components of a laptop computer have the following joint probability density function for their useful lifetimes X and Y (in years): f(x,y) = a. Find the marginal probability density function of X, fx(x). Enter a formula below. Use for multiplication, / for division, A for power and exp for exponential function. For example, otherwise 3*xA3 exp(-x/3) means 3x3e3 X 2 0 Submit Answer Incorrect. Tries 3/10 Previous Tries b. Find the...
Mathematical Statistics แ (Homework y 5) 1. Let , be a random sample fiom the densit where 0 s θ ...
difficult……
2and4 thanks
Mathematical Statistics แ (Homework y 5) 1. Let , be a random sample fiom the densit where 0 s θ 1 . Find an unbiased estimator of Q 2. Let Xi, , x. be independent random variables having pdfAx; t) given by Show that X is a sufficient statistic for e f(xl A) =-e- . x > 0 3. Let Xi, , x,' be a random sample from exponential distribution with (a) Find sufficient statistic for λ....
Mathematical Statistics แ (Homework y 5) 1. Let , be a random sample fiom the densit where 0 s θ ...
Mathematical Statistics แ (Homework y 5) 1. Let , be a random sample fiom the densit where 0 s θ 1 . Find an unbiased estimator of Q 2. Let Xi, , x. be independent random variables having pdfAx; t) given by Show that X is a sufficient statistic for e f(xl A) =-e- . x > 0 3. Let Xi, , x,' be a random sample from exponential distribution with (a) Find sufficient statistic for λ. (b) Find an...
Please give detailed steps. Thank you. 2. Consider the following joint distribution of two discrete variables...
Please give detailed steps. Thank you.
2. Consider the following joint distribution of two discrete variables X and Y: fx,y(x, y) 01 2 3 お88 Recall that the marginal distribution of X is defined as: fx(x) and the marginal distribution of Y is defined as fy(v) -xf(i) Find fx(x) and fy(y) in the support of X and Y (or in simpler terms, find 1), P(Y = 0), P(Y-1), P(Y-2) and P(Y P(X-0), P(X 3)) b. The conditional density of Y...
Credit card fraud is fraud perpetrated through stolen credit cards or credit card information. For years, credit card issuers have been using data mining and statistical tools to detect fraud. Citiba...
Credit card fraud is fraud perpetrated through stolen credit cards or credit card information. For years, credit card issuers have been using data mining and statistical tools to detect fraud. Citibank reported that knowing the type of product or service bought, frequency of purchases, and size and location of transaction can significantly reduce fraud. (Source: Jesus Mena, Investigative Data Mining for Security and Criminal Detection, Butterworth-Heinemann, pp. 250-251) A data-mining analyst at a major credit card company would like to...
I don't understand a iii and b ii, What's the procedure of deriving the limit distribution? Thanks. 6. Extreme...
I don't understand a iii and b ii, What's the procedure of
deriving the limit distribution? Thanks.
6. Extreme values are of central importance in risk management and the following two questions provide the fundamental tool used in the extreme value theory. (a) Let Xi,... , Xn be independent identically distributed (i. i. d.) exp (1) random variables and define max(Xi,..., Xn) (i) Find the cumulative distribution of Zn (ii) Calculate the cumulative distribution of Vn -Zn - Inn (iii)...
8. You are given two boxes, one contains nuts and the other contains bolts. Below is...
8. You are given two boxes, one contains nuts and the other contains bolts. Below is a picture of a bolt. The D indicates Below right is a side and overhead picture of a nut. The the diameter of the bolt D indicates the diameter of the hole INSIDE the nut. ATI RODI c ISO METRIC AND WASHERS A bolt is supposed to fit inside a nut. On the right is a picture of a bolt properly fitting inside a...
Return to the original model. We now introduce a Poisson intensity parameter X for every time point and denote the parameter () that gives the canonical exponential family representation as above by...
Return to the original model. We now introduce a Poisson intensity parameter X for every time point and denote the parameter () that gives the canonical exponential family representation as above by θ, . We choose to employ a linear model connecting the time points t with the canonical parameter of the Poisson distribution above, i.e., n other words, we choose a generalized linear model with Poisson distribution and its canonical link function. That also means that conditioned on t,...
part b and c In class we derived a Fokker-Planck equation for the velocity distribution P(et)...
part b and c
In class we derived a Fokker-Planck equation for the velocity distribution P(et) starting from the assumption of small random changes in velocity at each time step f.(t) where f(t) is chosen from a distribution WU: ). Einstein's original approach to Brownian motion had a different starting point, focusing on position differences at each time step x(t + Δt)-x(t) + E(t) where £(t) is a random displacement chosen from some distribution W(E). Underlying this ap- proach is...
A device runs until either of two components fails, at which time the device stops running. The joint probability density function of the lifetimes of the two components, both measured in hours, is given by Ш for 0 < z < 3 and 0SyS3, xy(,y)27 0 otherwise. (a) 6 points Find the marginal probability density function for the random variable X. (b) [8 points] Are X and Y independent random variables? Justify your answer. (c) 6 points] Calculate the probability...
need help for a and c. Thank you!
Two components of a laptop computer have the following joint probability density function for their useful lifetimes X and Y (in years): f(x,y) = a. Find the marginal probability density function of X, fx(x). Enter a formula below. Use for multiplication, / for division, A for power and exp for exponential function. For example, otherwise 3*xA3 exp(-x/3) means 3x3e3 X 2 0 Submit Answer Incorrect. Tries 3/10 Previous Tries b. Find the...
difficult……
2and4 thanks
Mathematical Statistics แ (Homework y 5) 1. Let , be a random sample fiom the densit where 0 s θ 1 . Find an unbiased estimator of Q 2. Let Xi, , x. be independent random variables having pdfAx; t) given by Show that X is a sufficient statistic for e f(xl A) =-e- . x > 0 3. Let Xi, , x,' be a random sample from exponential distribution with (a) Find sufficient statistic for λ....
Mathematical Statistics แ (Homework y 5) 1. Let , be a random sample fiom the densit where 0 s θ 1 . Find an unbiased estimator of Q 2. Let Xi, , x. be independent random variables having pdfAx; t) given by Show that X is a sufficient statistic for e f(xl A) =-e- . x > 0 3. Let Xi, , x,' be a random sample from exponential distribution with (a) Find sufficient statistic for λ. (b) Find an...
Please give detailed steps. Thank you.
2. Consider the following joint distribution of two discrete variables X and Y: fx,y(x, y) 01 2 3 お88 Recall that the marginal distribution of X is defined as: fx(x) and the marginal distribution of Y is defined as fy(v) -xf(i) Find fx(x) and fy(y) in the support of X and Y (or in simpler terms, find 1), P(Y = 0), P(Y-1), P(Y-2) and P(Y P(X-0), P(X 3)) b. The conditional density of Y...
Credit card fraud is fraud perpetrated through stolen credit cards or credit card information. For years, credit card issuers have been using data mining and statistical tools to detect fraud. Citibank reported that knowing the type of product or service bought, frequency of purchases, and size and location of transaction can significantly reduce fraud. (Source: Jesus Mena, Investigative Data Mining for Security and Criminal Detection, Butterworth-Heinemann, pp. 250-251) A data-mining analyst at a major credit card company would like to...
I don't understand a iii and b ii, What's the procedure of
deriving the limit distribution? Thanks.
6. Extreme values are of central importance in risk management and the following two questions provide the fundamental tool used in the extreme value theory. (a) Let Xi,... , Xn be independent identically distributed (i. i. d.) exp (1) random variables and define max(Xi,..., Xn) (i) Find the cumulative distribution of Zn (ii) Calculate the cumulative distribution of Vn -Zn - Inn (iii)...
8. You are given two boxes, one contains nuts and the other contains bolts. Below is a picture of a bolt. The D indicates Below right is a side and overhead picture of a nut. The the diameter of the bolt D indicates the diameter of the hole INSIDE the nut. ATI RODI c ISO METRIC AND WASHERS A bolt is supposed to fit inside a nut. On the right is a picture of a bolt properly fitting inside a...
Return to the original model. We now introduce a Poisson intensity parameter X for every time point and denote the parameter () that gives the canonical exponential family representation as above by θ, . We choose to employ a linear model connecting the time points t with the canonical parameter of the Poisson distribution above, i.e., n other words, we choose a generalized linear model with Poisson distribution and its canonical link function. That also means that conditioned on t,...
part b and c
In class we derived a Fokker-Planck equation for the velocity distribution P(et) starting from the assumption of small random changes in velocity at each time step f.(t) where f(t) is chosen from a distribution WU: ). Einstein's original approach to Brownian motion had a different starting point, focusing on position differences at each time step x(t + Δt)-x(t) + E(t) where £(t) is a random displacement chosen from some distribution W(E). Underlying this ap- proach is...
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 10 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 10 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 10 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 10 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 10 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 10 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 10 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 10 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 10 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 10 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 10 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 10 months ago