Question: 19. By using the moment-generating function of a random variable X having the binomial distribution with parameter p, show that the mean and the variance

19. By using the moment-generating function of a random variable X having the binomial distribution with parameter p, show that the mean and the variance of X are np and np(1 − p), respectively.

252 6 Distribution of Functions of Random Variables

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Probability Statistics Questions!

28. By using the moment-generating function (4.6.4) of a random variable X having the binomial distribution (4.6.2), show that the mean and variance of X are np and npq, respectively.

can you please help me with mathematical Statistics 1. /12 marks) Let X be a binomially distributed random variable with parameters n and p. i. (12 marks) Show that Var(X) = np(1 - p). (See hint on...

Moment The moment-generating function of the random variable X having a chi-squared distribution with v degrees of freedom is Mx(t)=(1-21) show that the mean and variance of the chi-squared...

Helpful hint: The following topics/concepts are covered in this homework, in no particular order (different problems cover different concepts): Class 6: Discrete Probability Distributions The...

(REALLY NEED HELP WITH QUESTIONS 1-11 WITH FULL EXPLANATIONS. HAND WRITTEN ANSWERS ARE PREFERRED IF AND WHEN POSSIBLE. NOTE: Week6-1.txt, Week6-2.txt, and Week6-3.txt are listed at the bottom of the...

(REALLY NEED HELP WITH QUESTIONS 1-11 WITH FULL EXPLANATIONS. HAND WRITTEN ANSWERS ARE PREFERRED IF AND WHEN POSSIBLE). (NOTE: Week6-1.txt, Week6-2.txt, and Week6-3.txt data is listed at the bottom...

3. Let Mx (t) be the moment-generating function of a random variable X and be the mean of X. (a) Show that the moment-generating function of (X ) is Mx- (t) = et Mx (t). (b) Show that the rth...

Accident records collected by an automobile insurance company give the following information: The probability that an insured driver has an automobile accident is 0.17; if an accident has occurred,...

Hello, I am struggling with these question is a activity that have 45 questions, but this are the ones that I don't know why I can't get them right. Thank you an advance. 2. [2.4/3 Points] DETAILS...

A binomial distribution has p = 0.22 and n = 75. a. What are the mean and standard deviation for this distribution? b. What is the probability of exactly 11 successes? c. What is the probability of...

Assume there are 1,500 SGBM/GBM students (all levels, all locations). Calculate the ideal sample size using both Krejcie and Morgans guidelines, and Roscoes Rule of Thumb

In the absence of a specific agreement, shares of stock are not freely transferable. a . True b . False

The monthly utility bills for a household in Riverside, California, were recorded for 12 consecutive months starting in January 2010: a. Construct a box plot for the monthly utility costs. b. What...