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.
1
f't""("')
,['.(
les
&
Binomial
DIStribution
Revisiopsss
»*Discrete
Random
Variab
Make
sure
you
show
all
steps
of
working
when
doing
these
questions.
\ﬂ
Find
the
value
of
a
for
l_hcrIbl»lfn}fggrw}_\hnhumy
distribution:
)
e
L
}
e
P

qu'wj,'mn
__lej:fQ,
_03
_\
Hence
find
Pr
(X<2)and
E(X).
@
A
random
\'arinlllq__\_'j)__%_!l\'c_
probability
di
striby
\
random
X
==
}
a
tion:
4
PrOX=x)
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
Yis
such
that
its
mean
is
10
and
its
standard
deviation
is
5.
Find
E(X")
Ls
A
discrete
random
variable
=
(&
A
game
is
Plﬂ)'cfi
by
selecting
coloured
cubes
from
a
box.
The
box
initially
contains
three
red
and
seven
b_\uc
cubes.
Mr
Cashino
pays
$10,00
each
time
he
selects
tWo
cubes.
If
he
gets
two
red
cubes,
he
gets
$20
prize
or
loss?
Is
this
a
fair
game?
I
not,
and
if
he
gets
one
red
cube,
he
gets
a
$10
prize.
What
is
his
expected
gain
what
should
Mr
Cashino
be
charged
to
play
the
game?
t
a
funfair.
Xhas
a
probability
distribution
as
LS)
A
random
variable
X
represents
the
points
scored
on
a
spinner
&
shown
below:

i
2
A
It
is
known
that
Var
(X)
is
equal
to
6.6.
Find:

(@)
aandb
(b)
E(GX2)
(c)
Var(3X
—2)
s
the
probability
that
they
score
at
least
5
points
exactly
twice?
A
person
spins
the
spinner
5
times.
What
i
d
dice
are
rolled
and
the
sum
of
the
two
dice
is
noted.
If
the
two
dice
are
rolled
ten
times,
what
is
ecimal
places)
exactly
three
times?
ss
than
5
times?
d
dice
are
rolled
ten
times.
If
the
sum
of
7is
is
obtained
no
less
than
5
times,
the
playe
@
Two
coloure
the
probability
(correct
todd
(2)
that
the
sum
of
the
two
dice
is
7
(b)
that
the
sum
of
the
two
dice
is
7
no
le
<~'
b
)
A
game
is
played
where
these
two
coloure
times,
the
player
wins
$5,
and
if
the
sum
of
7
they
have
to
pay
an
amount
$C.
().
IfGisthe
gain
obtained
by
the
player
playing
this
game,
much
C
is
for
the
game
to
be
a
fair
game.
obtained
exactly
three
r
wins
$10.
Otherwise,
construct
a
probability
distribution
table
for
G.
(d)
Hence
calculate
how