Exponential distribution with mean

Reference no: EM13966630

12. Let X, X1, X2, X3,... be random variables that are positive and integer valued. Show that Xn """ X if and only if for every integer k.

lim n→∞ P(Xn = k) = P(X = k)

13. Let Z1, Z2,... be iid random variables with density f . Suppose that P(Zi > 0) = 1 and that λ = limx↓0 f (x) > 0. Let Xn = n min{Z1,..., Zn}.Show that Xn """ Z where Z has an exponential distribution with mean 1/λ.

Reference no: EM13966630

Questions Cloud

What are the main sources of revenues for federal government : What are the main sources of revenues for the federal government? Before World War II, what was the key source of revenues of the federal government?

Problem regarding the percent con?dence interval : Estimate the cdf F (x). Compute and plot a 95 percent con?dence envelope for F (as described in the appendix). Find an approximate 95 percent con?dence interval for F (4.9) - F (4.3).

Diplomatic immunity and legislative immunity : Explain the distinction between diplomatic immunity and legislative immunity. Next, support or criticize the premise that diplomatic immunity is vital for Americans abroad

What is the shaft speed in radians per second : A flywheel with a moment of inertia of 4 kg × m2 is initially at rest. If a torque of 5 N × m (counterclockwise) is suddenly applied to the flywheel, what will be the speed of the flywheel after 5 s? Express that speed in both radians per second a..

Exponential distribution with mean : Let Z1, Z2,... be iid random variables with density f . Suppose that P(Zi > 0) = 1 and that λ = limx↓0 f (x) > 0. Let Xn = n min{Z1,..., Zn}.Show that Xn """ Z where Z has an exponential distribution with mean 1/λ.

How many possible sitting arrangements are there : How many possible ways can these 6 council members can be seated? How many possible sitting arrangements are there if only gender is considered in the process?

What are the goals and objectives for the organization : The marketing plan format is one that is utilized by major corporations all over the country. However, writing a comprehensive marketing plan is a difficult and challenging task, yet, the ability to write such a plan is critical to the development..

Description of the historical development of police agencies : Write a 1,050- to 1,750-word paper in which you include the following: A description of the historical development of police agencies and The main types of law enforcement agencies

The role of the police in today society : Create a 8- to 10-slide Microsoft PowerPoint presentation, including speaker notes, in which you include the following: The role of the police in today's society

User Account

All Pages