Question

The joint PMF,
p
X
,
Y
(
x
,
y
)
, of the random variables
X
and
Y
is given by the following table:


y
=
1

4
c

0

2
c

8
c

y
=
0

3
c

2
c

0

2
c

y
=
−
1

2
c

0

c

4
c

x
=
−
2

x
=
−
1

x
=
0

x
=
1

Answer 1

how about reformatting your text so it makes some sense?

Answer 2

The joint PMF, 𝑝𝑋,𝑌(𝑥,𝑦), of the random variables 𝑋 and 𝑌 is given by the following table:

𝑦=1 4𝑐 0 2𝑐 8𝑐
𝑦=0 3𝑐 2𝑐 0 2𝑐
𝑦=−1 2𝑐 0 𝑐 4𝑐
𝑥=−2 𝑥=−1𝑥=0 𝑥=1

c=?
pX(1)=?
if 𝑍=𝑋2𝑌3 then 𝐄[𝑍∣𝑌=−1] = ?
Conditioned on the event that 𝑌≠0 , are 𝑋 and 𝑌 independent?
𝖵𝖺𝗋(𝑌∣𝑋=0)= ? if X=0