Explain moment generating functions and poisson process

Reference no: EM13122433

Probability: Moment Generating Functions and Poisson Process

Let X be a discrete random variable with probability mass function Pr {X=k} = c(1+ k^2) for k= -2, -1, 0, 1, 2.
a) Determine c.
b) Determine Pr {X <= 0}
c) Determine the mean of X
d) Why is the previous answer fairly obvious?
e) Determine the variance of X
f) Compute Pr {X=2 | X >= 0}
g) Determine the moment generating function of X

Let Y be a Poisson random variable with parameter 1.5
a) Compute Pr {Y=0}
b) Compute Pr {Y <= 1}
c) Compute Pr {Y=0 |Y <= 1}
d) What is E[Y]?
e) Determine the variance of Y
f) Determine the moment generating function

Suppose the random variable S has moment generating function of (q + p *(e^t))^n where q= 1- p, 0 < p < 1 and n is a positive integer. Find the mean and variance of Y.

Reference no: EM13122433

Questions Cloud

Excess of tax depreciation over book depreciation : Excess of tax depreciation over book depreciation, $40,000. This $40,000 difference will reverse equally over the years 2011-2014. Deferral, for book purposes, of $25,000 of rent received in advance. The rent will be earned in 2011.

What is the marginal rate of substitution for consumer : How much of each good does each consumer demand in equilibrium and what is the marginal rate of substitution for consumer A at the competitive equilibrium?

Slope-intercept form of perpendicular bisector : Find the slope-intercept form of a line that is the perpendicular bisector of a line segment connecting (-7,3) and (1,17)

Quadratic minimum maximum problems : A rope connects two poles that are 80 feet apart. The function .02x^2+15 models the height the rope is above the ground

Explain moment generating functions and poisson process : Probability: Moment Generating Functions and Poisson Process Let X be a discrete random variable with probability mass function Pr {X=k} = c(1+ k^2) for k= -2, -1, 0, 1, 2.

Information about slope intercept form : In the problem below, assume that the relationship can be expressed as a linear equation in two variables, and use the given information to determine the equation. Express the equation in slope-intercept form.

Promotional and accounting services : During the current year JET Industries issued 5 million of its $1 par common shares to its underwriters for $25,000,000 less promotional and accounting services of $500,000 to effect the issue.

English essay on friendship in the internet age : english essay Friendship in the Internet Age.write a 5-6 page research paper discussing and debating the topic. The paper must use at least 5 sources .

What is a break even point : What is a break even point? a) The level of operations at which a business revenues exceeds the budget. b) The level of operations at which the business will be able to break into a new market

User Account

All Pages