An Internet router can send packets via route 1 or route 2. The packet
delays on each route are independent eap random variablesl and so the difference in
delay between route 1 and route 2, denoted by X, has a LaplaceL density. Find
P[3HEDIUEXE3-
Sotmion.

In very similar way also maybe obtained such continuous version of
formula of total probability (*) and Bayes' formula (*)
(*)
(*)
and using (*) we get
Bayes' formula (*)
(*)
and from formula of total probability
to reflect our knowledge about experiment

5.1 Joint Cumulative Distribution Functions
149
function of both x and y. Note that since the event X must happen, then
cfw_X cfw_Y y = cfw_Y y so that FX,Y (, y) = FY (y). Likewise, FX,Y (x, ) =
FX (x). In the context of joint CDFs, FX (x) and FY (y) ar

Let X. Y, and Z be independent random variables: where X is Bernoulli
with parameter 1 /3, Y is exponential with parameter 2, and Z is Poisson with param
eter 3.
(a) Consider the new random variable U = XY + (1 - X)Z. Find the transform
associated with U.