Alice
passes
through
four
traffic
lights
on
her
way
to
work,
and
each
light
is
equally
likely
to
be
green
or
red,
independently
of
the
others.
(a)
What
is
the
PMF,
the
mean,
and
the
variance
of
the
number
of
red
lights
that
Alice
encounters?
(b)
Suppose
that
each
red
light
delays
Alice
by
exactly
two
minutes.
What
is
the
variance
of
Alice’s
commuting
time?
a) X = no of red lights passed. X is binomially distributed with n=4, p=0.5.
Mean = np = 2
Var = np(1-p)=1
PMF = nCk * 0.5^ k * 0.5 ^ (4-k)
Problem lies in b. I thought the variance would be the same as variance of X.
.: Var(time) = 1 * 2 minutes
But the answer was Var(2X) = 2^2*Var(X) =4
Can you explain?
Best Answer
It's because $Var(aX+b) = a^2 Var(X)$, here your $a=2$.