Let X? - x? (1, µ²) and X, ~ N (4,, 0}). Find:(i) the probability distribution funciton (pdf) and moment-generating funciton (mgf) of 2X, – 1.(ii) the pdf of E(2X+1+ X,42 – 1) where the X, are independent, µ1 = 42 = 1, H3 = 3, µ4 = 4,%3DHs = 5, of = a} = 1, ož = o; = 4 and o} = 2.(iii) Identify the distribution in 2(i) and (ii).

Answered: the probability par) generat (mgf) (ii)…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 1E

See similar textbooks

Similar questions

let x be a random variable with moment generating function Mx(t)=(0.6 + 0.4e^t)^20 then the variance of x is
Suppose that Y1,Y2 are independent identically distributed (iid) random variables form a random sample from a probability distribution given by f(y)=θe^(−θy), y≥0 Suppose we observed a sample of size two (n=2): 0.04304550, 0.50263474. Read the data into R. Create a function in R to compute the log‐likelihood. Plot the likelihood function on a fine grid of θ values in R. Estimate the MLE of θ using Bisection, Secant, and Newton-Raphson methods in R.
Calculate the mean and variance when the probability variable X's moment-generating function is as follows f(x)= 2x-1/16 , x=1,2,3,4 my answer is mean = 25/8, var = 170/16 - (50/16)^2 but solution is mean = 2, var = 4/5 How do we solve the problem? Help me
The time (in hours) required to repair a machine is exponentially distributed 1 with parameter 2 = = what is the probability that the repair time exceeds 3 3
Q5 Find the variance for the PDF px(x) = e-«/2, x > 0.
Suppose that n observations are chosen at random from a continuous pdf fY(y). What is the probability that the last observation recorded will be the smallest number in the sample?
Let X and Y be independent Exp(2) random variables. Define W = X + Y. a) Determine the correlation between X and W. The joint pdf of X and W is: fx,w(x, w) = 1^(2) e^(-1w) I{O
(3) Let X = b >(8,-) find E(5+6x) and distribution function.
Suppose that the random change in value of a financial asset is X over the first day and Y over the second. Suppose also that Var(X) =18 and Var(Y) = 26 In this case, the total change in the value over these two days is given by X +Y. Do you have enough information to compute Var(X +Y)? If so, compute this value. If not, explain what additional information you need to do so.
Let X be a continuous random variable whose moment generating function is 4x(t) = (5) ³. Find Var (X)
At the end of summer, the total weight of seeds accumulated by a nest of seed-gathering ants will vary from nest to nest. If the total weight of seeds accumulated by a nest is exponentially distributed with parameter λ = 1/5, (a) What is the probability that the total combined weight of the seeds gathered by 100 nests will be larger than 4 95 pounds by the end of next summer? (b) What is the probability that the average weight of the seeds gathered by the 100 nests is larger than 5.3 ? (c) What assumptions are you making to answer parts (a) and (b)? Do you think those assumptions make sense in the context of this problem? Explain. (d) Tell us about the possibility that the total combined weight of the seeds gathered by 2 nests follows a normal distribution. Justify your answer in the speciﬁc context of this problem (ants, nests, seed-gathering). That is, do not just make generic statements that you think apply to every context in the world.
Identify the distributions of the random variables with the moment- generating functions shown below. For each random variable also indicate what the mean and the variance are. a) m(t) = e^2.2(e^t−1)b) m(t) = 1/(1 − 2t)^2 c) m(t) =( e^5t−e^t )/4t

SEE MORE QUESTIONS

Recommended textbooks for you

Calculus For The Life Sciences

Calculus

ISBN:

9780321964038

Author:

GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:

Pearson Addison Wesley,

Calculus For The Life Sciences

Calculus

ISBN:

9780321964038

Author:

GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:

Pearson Addison Wesley,

SEE MORE TEXTBOOKS

the probability par) generat (mgf) (ii) the pdf of (2X,41+ X,+2 – 1) where the X, are independent, µ1 = µ2 = 1, µ Hs = 5, of = a} = 1, ož = o; = 4 and ož = 2. (iii) Identify the distribution in 2(i) and (ii).