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sDjscrete
Random
Variables
&
Binomial
Distribution
Reyisjopss
Make
sure
you
show
all
steps
of
working
when
doing
these
questions
\_D
Find
the
value
of
a
for
the
following
probability
distribution:
s
0

e
i).

2a

da
Hence
find
Pr(X'<
2)
and
E(X).
able
X
has
the
probability
distribution:
2
A
random
vari
X
D
Find:
()
the
constant
k
(b)
the
most
likely
value
of
X
(a)
E(X),
the
expectation
of
X'
(b)
Var(X),
the
variance
of
X
A
discrete
random
variable
X
is
such
that
its
mean
is
10
and
its
standard
deviation
is
5.
Find
E(X
.
)
tially
contains
three
red
and
seven
blue
gets
two
red
cubes,
he
gets
a
$20
prize
s?
Is
this
a
fair
game?
If
not,
A
game
is
played
by
selecting
coloured
cubes
from
a
box.
The
box
ini
cubes.
Mr
Cashino
pays
$10.00
each
time
he
selects
two
cubes.
If
he
and
if
he
gets
one
red
cube,
he
gets
a
$10
prize.
What
is
his
expected
gain
or
los
what
should
Mr
Cashino
be
charged
to
play
the
game?
A
random
variable
X
represents
the
points
scored
on
a
spinner
at
a
funfair.
X
has
a
probability
distribution
as
shown
below:
x
2
3
;'
a
Pr(X
=x)
0.2
It
is
known
that
Var
(X)
is
equal
to
6.6.
Find:
aand
b
EGX2)
Var(3X
—2)
A
person
spins
the
spinner
5
times.
What
is
the
probability
that
they
score
at
least
5
points
exactly
twice?
Two
coloured
dice
are
rolled
and
the
sum
of
the
two
dice
is
noted.
If
the
two
dice
are
rolled
ten
times,
what
is
the
probability
(correct
10
4
decimal
places)
that
the
sum
of
the
two
dice
is
7
exactly
three
times?
that
the
sum
of
the
two
dice
is
7
no
less
than
5
times?
A
game
is
played
where
these
two
coloured
dice
are
rolled
ten
times.
If
the
sum
of
7
is
obtained
exactly
three
times,
the
player
wins
$5,
and
if
the
sum
of
7
is
obtained
no
less
than
5
times,
the
player
wins
$10.
Otherwise,
they
have
to
pay
an
amount
$C.
If
G
is
the
gain
obtained
by
the
player
playing
th
Hence
calculate
how
much
C
is
for
the
game
to
be
a
fair
game.
is
game,
construct
a
probability
distribution
table
for
G.