Question: A random variable X has the Poisson distribution (a) Show that the moment-generating function is (b) Use MX (t) to fi nd the mean and

A random variable X has the Poisson distribution

f(x) = х%3D0,1,... x!

(a) Show that the moment-generating function is
Mx(t)= e(d-1)

(b) Use MX (t) to fi nd the mean and variance of the Poisson random variable.

f(x) = %3D0,1,... x! Mx(t)= e(d-1)

Step by Step Solution

★★★★★

3.24 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a b Mx... View full answer

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 Applied Statistics and Probability Questions!

Q:

Suppose that a random variable X has the Poisson distribution with unknown mean >0. Find the Fisher information I () in X.

Q:

Suppose that a random variable X has the Poisson distribution with unknown mean ( > 0). Show that the only unbiased estimator of e2 is the estimator (X) such that (X) = 1 if X is an even integer and...

Q:

A random variable X has the Poisson distribution p(x; ?) = e ?? ? ? /x for x = 0, 1, 2, Show that the moment-generating function of X is using Mx(t), find the mean and variance of the Poisson...

Q:

7.19 A random variable X has the Poisson distribution p(x; ) = e x /x! for x = 0, 1, 2, . . . . Show that the moment-generating function of X is MX (t) = e(e t 1) . Using MX (t), find the mean and...

Q:

A random variable X has the Poisson distribution p(x; ) = e /x! for x = 0, 1, 2, . Show that the moment-generating function of X is x 1 X x Using M (t), find the mean and variance of the Poisson...

Q:

A random variable X has the Poisson distribution p(x; ) = ex/x! for x = 0, 1, 2,... . Show that the moment-generating function of X is MX(t) = e (et1). Using MX(t), find the mean and variance of the...

Q:

(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...

Q:

MUST BE CORRECT ANSWERS A small software company has the following simplified cashflow, funded by shareholders' equity of 20,000 and a bank overdraft of 5000: Invoiced money received 2 months after...

Q:

(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...

Q:

MA677 - problem set 1 1. You model the production of a weaving machine in terms of meters of ribbon produced per minute. Mean production in a one minute interval is 1.2 m with standard deviation of...

Q:

What is the effect on a firms breakeven point of a lower income tax rate?

Q:

A Thermodynamic Process in a Solid. A cube of copper 2.00 cm on a side is suspended by a string. (The physical properties of copper are given in Tables 14.1, 17.2, and 17.3.) The cube is heated with...

Q:

Simplify each of the following, leaving your answer in positive index form. (a) mxm (b) b) (pq) + (pq) 10 32x (c) 15

Q:

8 Explain why gold backing is not necessary to give paper money value.

Q:

Reanalyze the data in Table 10.49 using the Wilcoxon rank sum test? Table 10.49: Outcome data for the Sorbinil Retinopathy Trial (n = 481) change in retinopathy level A more efficient method of...

Q:

Compare your results in Problems 10.149 and 10.151. Which do you think is a better method of analysis? A more efficient method of analysis would leave the change in retinopathy level in its raw form...

Q:

Fit a regression line relating the percentage of reticulocytes (x) to the number of lymphocytes (y)? Hematology The data in Table 11.17 are given for 9 patients with aplastic anemia [11]. Table...

Q:

Ricky Ripovs Pawn Shop charges an interest rate of 15.75 percent per month on loans to its customers. Like all lenders, Ricky must report an APR to consumers. Requirement 1: What rate should the shop...

Q:

Lights Incorporated calculates cost for an equivalent unit of production using the weighted-average method. Data for July: Work-in-process inventory, July 1 (37,500 units): Direct materials (97%...

Q:

When a scientist conducted a genetics experiment withpeas, one sample of offspring consisted of 911 peas, with 708 of them having red flowers. If we assume, as the scientist did, that under...