Question

Poisson Distribution: p(x, λ)  =   λx  exp(-λ) /x!  ,  x = 0, 1, 2, ….. Find the moment generating function Mx(t)...

  1. Poisson Distribution: p(x, λ)  =   λx  exp(-λ) /x!  ,  x = 0, 1, 2, …..

  1. Find the moment generating function Mx(t)

  1. Find E(X) using the moment generating function

2. If X1 , X2 , X3  are independent and have means 4, 9, and 3, and variencesn3, 7, and 5. Given that Y = 2X1  -  3X2  + 4X3. find the

  1. mean of Y
  2. variance of  Y.

3. A safety engineer claims that 2 in 12 automobile accidents are due to driver fatigue. Using the formula for Binomial Distribution find the probability that at least 3 of 5 automobile accidents are due to driver fatigue.

4. The number of complaints that a dry-cleaning establishment receives per day is a random variable having   Poisson distribution with λ = 1.8.  Use Poisson distribution formula to find the probability that there will be at most  two complaints on any given day.       

5.

i. Define Geometric distribution.

  1. Show that it is a distribution

  1. Find the moment generating function for Geometric distribution

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Given the exponential distribution f(x) = λe^(−λx), where λ > 0 is a parameter. Derive the...
Given the exponential distribution f(x) = λe^(−λx), where λ > 0 is a parameter. Derive the moment generating function M(t). Further, from this mgf, find expressions for E(X) and V ar(X).
The moment generating function for the random variable X is MX(t) = (e^t/ (1−t )) if...
The moment generating function for the random variable X is MX(t) = (e^t/ (1−t )) if |t| < 1. Find the variance of X.
(i) If a discrete random variable X has a moment generating function MX(t) = (1/2+(e^-t+e^t)/4)^2, all...
(i) If a discrete random variable X has a moment generating function MX(t) = (1/2+(e^-t+e^t)/4)^2, all t Find the probability mass function of X. (ii) Let X and Y be two independent continuous random variables with moment generating functions MX(t)=1/sqrt(1-t) and MY(t)=1/(1-t)^3/2, t<1 Calculate E(X+Y)^2
Suppose that the moment generating function of a random variable X is of the form MX...
Suppose that the moment generating function of a random variable X is of the form MX (t) = (0.4e^t + 0.6)8 . What is the moment generating function, MZ(t), of the random variable Z = 2X + 1? (Hint: think of 2X as the sum two independent random variables). Find E[X]. Find E[Z ]. Compute E[X] another way - try to recognize the origin of MX (t) (it is from a well-known distribution)
Use the moment generating function Mx(t) to find the mean u and variance o^2. Do not...
Use the moment generating function Mx(t) to find the mean u and variance o^2. Do not find the infinite series. Mx(t) = e^[5*((e^t)-1)]
Let Z~N(0;1) and Y=Z^2. Find the cumulative distribution function, probability density function, and moment generating function...
Let Z~N(0;1) and Y=Z^2. Find the cumulative distribution function, probability density function, and moment generating function of Y.
The random variable X has moment generating function ϕX(t)=exp((9t)^2)/2)+15t) Provide answers to the following to two...
The random variable X has moment generating function ϕX(t)=exp((9t)^2)/2)+15t) Provide answers to the following to two decimal places (a) Evaluate the natural logarithm of the moment generating function of 2X at the point t=0.62. (b) Hence (or otherwise) find the expectation of 2X. c) Evaluate the natural logarithm of the moment generating function of 2X+7 at the point t=0.62.
Find P(X≤0) if the random variable X has a Poisson distribution such that P(X=1)=P(X=2).
Find P(X≤0) if the random variable X has a Poisson distribution such that P(X=1)=P(X=2).
A Poisson distribution has λ = 4.7.   (a )[2] Use the Excel function POISSON.DIST() and 5...
A Poisson distribution has λ = 4.7.   (a )[2] Use the Excel function POISSON.DIST() and 5 decimals to fill in the following table: 4 x 0 1 2 3 4 5 6 7 8 9 10 11 12+ P(x) (b)[2] Use a column chart to visualize the probability distribution above. How is it skewed? (c)[1] Find P(x ≤ 3). [steps & result] (d)[1] Find P(x ≥ 7). [steps & result] (e)[2] Find P(5 < x ≤ 9). [steps & result]...
Given a random variable X~exp(5). Z=(X-2)3 1. Find the distribution function FZ(t). 2. Find fz(t).
Given a random variable X~exp(5). Z=(X-2)3 1. Find the distribution function FZ(t). 2. Find fz(t).
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT