HomeworkLib
Question

If you graph some Gamma(α,β) densities, you will notice that in some cases as t increases...

If you graph some Gamma(α,β) densities, you will notice that in some cases as t increases they increase from zero, reach a maximum, and then decrease. Use elementary calculus to find, forα >1, the value of t for which the density reaches a maximum. (This value of t is called the mode of the distribution.)

math   Statistics-And-Probability   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

0 0
Add a comment
Know the answer?
Add Answer to:
If you graph some Gamma(α,β) densities, you will notice that in some cases as t increases...
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. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • 1. Suppose that Y ∼ Gamma(α, β) and c > 0 is a constant. (a) Derive the density function of U ...

    1. Suppose that Y ∼ Gamma(α, β) and c > 0 is a constant. (a) Derive the density function of U = cY. (b) Identify the distribution of U as a standard distribution. Be sure to identify any parameter values. (c) Can you find the distribution of U using MGF method also? I. Suppose that Y ~ Gamma(α, β) and c > 0 is a constant. (a) Derive the density function of U cY. (b) Identify the distribution of U...

  • 9. (9 pts) The random variable r-Gamma(x-2, β-4). functions to prove that the moment generating function...

    9. (9 pts) The random variable r-Gamma(x-2, β-4). functions to prove that the moment generating function for the random variable W mw(t) (1-12t)2. Use the method of moment-generating 3Y +5is eSt 10, (9 pts) Suppose that Y has a gamma distribution with α-n/2 for some positive integer n and β equal to some specified value. Use the method of moment-generating functions to prove that W- 2Y /g has a Chi-squared distribution with n degrees of freedom. Make sure you show...

  • Consider the log logistic CDF F(t)=1/(1+(t/α)-β) Find f(t), S(t), h(t), and H(t). It can be shown...

    Consider the log logistic CDF F(t)=1/(1+(t/α)-β) Find f(t), S(t), h(t), and H(t). It can be shown that h(t) can be non-monotone for some parameter choices. For these choices, it starts off at 0 for t=0, increases fairly rapidly to a maximum, and then gradually asymptotes out to 0 as t goes to infinity. Briefly describe in words what this would mean to a patient if T was the survival time after contracting a disease.

  • Suppose observations X1, X2,.. are recorded. We assume these to be conditionally independent and exponen- tially...

    Suppose observations X1, X2,.. are recorded. We assume these to be conditionally independent and exponen- tially distributed given a parameter θ: Xi ~' Exponential(θ), for all i 1, . . . , n. The exponential distribution is controlled by one rate parameter θ > 0, and its density is for r ER+ 1. Plot the graph of p(x:0) for θ 1 in the interval x E [0,4] 2. What is the visual representation of the likelihood of individual data points?...

  • Can someone please explain this problem in detail. 6. If you look at some of graphs...

    Can someone please explain this problem in detail. 6. If you look at some of graphs of the gamma distribution for various values of the parame- ters (α, β) (for example the ones at http://upload. wikimedia.org/wikipedia/commons/e/e6/ Gamma_distribution pdf.svg ), you'll see that the graphs (mostly) tend to look "single-peaked" They start small, increase until they reach a maximum, then decrease thereafter. Show that as long as α > l this is indeed what happens, where is the peak located, in...

  • Table 4             Regression Model             Y = α X1 + β X2             Parameter

    Table 4             Regression Model             Y = α X1 + β X2             Parameter Estimates                                     Coefficient        Standard Error             Constant               12.924                  4.425             X1                         -3.682                 2.630             X2                        45.216                12.560             Analysis of Variance             Source of         Degrees            Sum of             Mean             Variation           of Freedom       Squares            Square             F             Regression       XXX                 4,853                2,426.5             XXX             Error                 XXX                 485.3    Find above partial statistical output...

  • Table 4             Regression Model             Y = α X1 + β X2             Parameter

    Table 4             Regression Model             Y = α X1 + β X2             Parameter Estimates                                     Coefficient        Standard Error             Constant               12.924                  4.425             X1                         -3.682                 2.630             X2                        45.216                12.560             Analysis of Variance             Source of         Degrees            Sum of             Mean             Variation           of Freedom       Squares            Square             F             Regression       XXX                 4,853                2,426.5             XXX             Error                 XXX                 485.3    Find above partial statistical output...

  • 3. The graph below has axes to show the population sizes of a predator and its...

    3. The graph below has axes to show the population sizes of a predator and its prey. The dashed lines are the predator and prey isoclines. Prey Population Starting at the circle, draw in what will happen to the two populations if they are following the pattern in the Lotka-Volterra model of predation. (Remember that BOTH predator and prey numbers are represented by a point on the graph.) Use a series of arrows to show what happens. 2. Imagine two...

  • MATLAB MATLAB MATLAB Model description The logistic map is a function that is often used to...

    MATLAB MATLAB MATLAB Model description The logistic map is a function that is often used to model population growth. It is defined by P(t+1) = rP(t) (1 -P(t)/K) Here, P(t) represents the density of a population at year 1, the parameter r is a growth rate and the parameter K is the maximum possible population density (known as the carrying capacity). This equation says that if we know the density at one year, we can substitute it into the right-hand...

  • Physics 2: Dipole Moment and Electric Potential Having a hard time with some of these questions....

    Physics 2: Dipole Moment and Electric Potential Having a hard time with some of these questions. Help would be greatly appreciated. If you could put in all equations used and show your work it would be greatly appreciated. I want to compare the answers I got. You will be rewarded! Thanks :-) A long cylindrical conductor shell has a uniform positive charge distribution per unit length, +2 lambda and with inner radius r and the outer radius 2r.A long wire...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT