Question

Define a random process. Identify the type of random process for the following stochastic process.
(a) {Wk; k ∈ T} where Wk be the time that the kth customer has to wait in the system before
service.
(b) The price of a share observed over days.
(c) {Y (t);t ∈ T} where Y (t) denotes the number of phone calls recorded in the system at time
t.

Answer 1

for query in above, comment.

A random process / stochastic process na family of random variables {xy where to takes value in the index/ time set T. The collection of value of x denoted by s is called the state space To countable the random proses is dicrete. . . parameter stochastic process sis countable > random process is dicrete to s itale process Tin uncountable random proces in continuous time proces, we s is uncountable - 7 seal valued proces. (2) Ј4ело т-1,2,2, - ч . cour+able ... s=50,8) c R as waiting time is non-negative > The proces is discrete time seal valued Procem (0) Here T={1,2,..4 in countable as prices are reported for each day in s=00,00) CR is uncountable as price is non-negative - The proces is dicrete time real valued a process - T=(0,00) in uncountable s={0,1,2, - 4. in countable as no. of phone calls T Y si non- negative e