Question

In: Statistics and Probability

Let ξ and η be independent of each other, ξ follows the poisson distribution, and η...

Let ξ and η be independent of each other, ξ follows the poisson distribution, and η follows N (0,1).

Prove that ξ + η is a continuous random variable

Solutions

Expert Solution

Here elwe have given two random variable and we have to show that there sum is a continuous variate.


Related Solutions

) Let X1, . . . , Xn be iid from the distribution with parameter η...
) Let X1, . . . , Xn be iid from the distribution with parameter η and probability density function: f(x; η) = e ^(−x+η) , x > η, and zero otherwise. 1. Find the MLE of η. 2. Show that X_1:n is sufficient and complete for η. 3. Find the UMVUE of η.
The number of complaints received by a company each month follows a Poisson distribution with mean...
The number of complaints received by a company each month follows a Poisson distribution with mean 6. (a) Calculate the probability the company receives no complaint in a certain week. (b) Calculate the probability the company receives more than 4 complaints in a 2-week period. (c) Over a certain month, calculate the probability the company receives fewer complaints than it usually does with respect to its monthly average.
Consider a mathematical pendulum with a support point moving both in vertical (ξ(t)) and horizontal (η(t))...
Consider a mathematical pendulum with a support point moving both in vertical (ξ(t)) and horizontal (η(t)) direction. (a) Write the Lagrangian and determine the equation of motion. Hint: Consider two dimensions. (b) Consider small angle approximation. What are the linearized equations of motion? Discuss two cases: 1. uniformly accelerated vertical motion, 2. periodic horizontal motion
Suppose that the random variables, ξ, η have joint uniform density f(x, y) = 2/9 in...
Suppose that the random variables, ξ, η have joint uniform density f(x, y) = 2/9 in the triangular region bounded by the lines x = -1 , y - -1 and y = 1 - x. a) Find the marginal densities f(x) =∫ 2/9 dy (limits, -1 to 1-x) and f(y) =∫ 2/9 dx (limits -1 to 1-y). Also show that f(x) f(y) ≠ f(x, y) so that ξ and η are not independent. b) Verify that μξ = ∫...
The number of views of a page on a Web site follows a Poisson distribution with...
The number of views of a page on a Web site follows a Poisson distribution with a mean of 1.5 per minute. (i) What is the probability of no views in a minute? (ii) What is the probability of two or fewer views in 10 minutes? (iii) What is the probability of two or fewer views in 2 hours?
Let Ul , U2 , U3 , U4 , U5 be independent, each with uniform distribution...
Let Ul , U2 , U3 , U4 , U5 be independent, each with uniform distribution on (0,1). Let R be the distance between the minimum and the maximum of the Ui's. Find a) E(R); b) the joint density of the minimum and maximum of the U;'s; c) P(R> 0.5) Please do b) and c) and explain in details.
Occurring a bug in software follows poisson distribution(mean = 100). Each bug becomes an error independently...
Occurring a bug in software follows poisson distribution(mean = 100). Each bug becomes an error independently after certain time which follows exponential distribution(mean = 10). When an error appears in system, it will be eliminated immediately. (1) After 100 hours, find probability that number of eliminated errors is 5 (2) Find the expected number of bugs still remain in software. (Solving process could be related to binomial distribution) Thanks in advance
The number of airplane landings at a small airport follows a Poisson distribution with a mean...
The number of airplane landings at a small airport follows a Poisson distribution with a mean rate of 3 landings every hour. 4.1 (6%) Compute the probability that 3 airplanes arrive in a given hour? 4.2 (7%) What is the probability that 8 airplanes arrive in three hours? 4.3 (7%) What is the probability that more than 3 airplanes arrive in a period of two hours?
Suppose the number of earthquakes occurring in an area approximately follows a Poisson distribution with an...
Suppose the number of earthquakes occurring in an area approximately follows a Poisson distribution with an average rate of 2 earthquakes every year. a.) Find the probability that there will be 1 to 3 (inclusive) earthquakes during the next year in this area. b.) Find the probability that there will be exactly 5 earthquakes during the next 3 year period. c.) Consider 10 randomly selected years during last century. What is the probability that there will be at least 3...
The number of people arriving at an emergency room follows a Poisson distribution with a rate...
The number of people arriving at an emergency room follows a Poisson distribution with a rate of 9 people per hour. a) What is the probability that exactly 7 patients will arrive during the next hour? b. What is the probability that at least 7 patients will arrive during the next hour? c. How many people do you expect to arrive in the next two hours? d. One in four patients who come to the emergency room in hospital. Calculate...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT