What is branching process? Give two real examples of branching process.
If P(s) and Pn(s) respectively is the probability generating function (pgf) of the i.i.d. random variables and the random variables {Xn}, where Xn+1 =
Then show that:
Pn(s) = Pn-1(P(s))
and Pn(s) = Pn-1(P(s)).
### Branching Process: Definition and Real-World Examples A branching process is a type of stochastic process that models the growth of populations, where each individual in one generation produces a random number of offspring in the next generation. The process continues recursively, leading to a branching tree structure. #### Two Real-World Examples of a Branching Process 1. Spread of a Virus: - __________ __________ ___ ____ _____ _____ ____ _____.
_____ ______ ________ ___ ____ __________ _________ __________ _____ __________ __________.
_______ ___ ___ _______ ___ ____ _____ _______.
______ ________ _____ _______ ___ ____ _________ __________ _____ ____ ______ _____.
_________ _____ _________ ________ ______ ______ ________ _______ ________.
_______ __________ _____ ______ ___.
____ _________ ____ ___ _______ _________ _______ _________ _________ ________ _____.
____ __________ _______ ____ _______ _____ _____ _________ _______ ____.
___ _______ _________ ____ ________ ___ ______ ________ _______ ____.
______ ________ __________ _______ _____ ________.
___ ___ ________ ______ ___ ___ ________ ____ _________ __________ _________ _____.
______ _____ ______ ______ ________ ________ ___ ______ ______.
_________ ____ ____ _________ ________ _____ __________ _______ ______.
________ ______ ______ _________ ______ ____ ________.
_________ __________ ___ _________ _______ _____ _____ ____ ___ _________ __________ ________.
______ _______ _________ _____ _____ ________ ____ _____ __________.
__________ _____ _________ ___ ____ ______ ________ __________ _____ ____.
________ ___ ______ ______ ___.
_____ ___ ____ ___ ____ __________ __________.
_______ ______ _____ __________ ______ _____ ______ __________ ___ ________ __________.
_______ _____ __________ _________ ______ ______.
_______ ______ ___ ________ ____.
_______ ___ ___ _______ _________ __________ ____ ________ ___.
_____ ______ _______ _________ ______ _______.
__________ ____ __________ ___ __________ ___ _____ ________.
_____ _______ ___ ____ _________ _________ ________.
_____ __________ ______ ____ __________.
____ ________ _____ ____ _____ _________ ____ _____.
______ ______ _______ __________ _________ ______ _________.
_________ ___ _______ _____ _________ _______ __________ ____ _________ _____ ___ _______.
_______ ______ ________ ____ ________ ____ __________ _________ _______ _________ _______ __________.
_________ ______ _________ __________ ______ ________ ____ _____ _____ ________ ________ ________.
____ ______ ________ ___ ______ _____ ______.
____ ____ ______ _____ ____ ______ ______ ________ ___ ________ _____.
___ _________ ____ ________ _________ ___ _____ ____ ______ ______ _______.
____ ___ ______.
Get Full Answer on WhatsApp
In an investigation related to a specific type of scores of men and women aged 65 to 70, the mean verbal and performance scores for 101 subjects were found to be:
The sample covariance matrix of the scores was
In order to test the null hypothesis that observations came from a population with mean
apply a suitable test statistic. You may consider α = 01.0 for the test.
In order to fit the regression line on a data set consisting of 34 pairs of values (z,y), the least square estimates of β1 and β2 are to be computed. From the data set, the following values are obtained:
Obtain the fitted regression line.
State whether the following statements are true or false. Justify your answer with a short proof or a counter example:
i) Although in one-step transition probability matrix, ,P of a Markov chain the sum of each row must necessarily be unity but in higher order transition probability matrices, . This rule is not necessary.
ii) For the joint pdf of random variables (X,Y) given by:
iii) Let the r.v. X follows the negative exponential distribution with parameterThen
iv) One of the examples of non-Poisson queuing system is the (M / G (:)1/ ∞ (FIF0) queuing model.
v) be a random sample from
then maximum likelihood estimators o
In order to fit the regression line y = β1 + β2 on a data set consisting of 34 pairs of values (z,y), the least square estimates of β1 and β2 are to be computed. From the data set, the following values are obtained:
Obtain the fitted regression line.
Distinguish between ‘Age Replacement’ and ‘Block Replacement’ policies. Let the lifetimes Y1 ,Y2 ,...., are independently and identically distributed random variables and follows negative exponential distribution with parameter 5. If lifetimes T > 0 and age replacement policy is to be employed, then:
i) find the mean renewal time and
ii) find the long-run average cost per unit time, given the costs C 4 1 = and C 6 2 = units of money.
For the (M/M/K) : (∞ / FIF )0 queuing model with arrival rate λ and service rate per service channel µ, obtain the steady-state probability of n customers in the system, P . n Hence or otherwise, find the probability that an arrival has to wait.
For the (M/M/K) : (∞ / FIF )0 queuing model with arrival rate λ and service rate per service channel µ, obtain the steady-state probability of n customers in the system, P . n Hence or otherwise, find the probability that an arrival has to wait.