Question

Need some probability guidance on this question.

Answer 1

Let X be the number of heads and Y be the number of tails in 5 coin tosses.
Let Z = X - Y. Express Z as a function of X.
So here's what I did so far...

Answer 2

if you flip 3 heads you flip also 2 tails

Answer 3

Oh and I forgot to mention that the coin is unfair and that you have a probability of 1/3 of getting a head.

Answer 4

What I have so far:
\[P(X=x) = \left(\begin{matrix}5 \\ x\end{matrix}\right)*(\frac{1}{3})^x*(1-\frac{1}{3})^{5-x} \]

Answer 5

ok but that has nothing to do with \(Z\) or \(X\)a nd \(Y\) they are just random variables that counts the number of heads, and difference between number of heads and tails

Answer 6

Same thing for P(Y=y) I guess only 2/3 and 1-2/3
What I'm confused about is what do they want me to do? Find P(Z=z)?

Answer 7

did you write Z in terms of X only?

Answer 8

Ohh Z=X-Y=X-(5-X)

Answer 9

`Express Z as a function of X`

X = number of heads
Y = number of tails
we flip the coin 5 times, so X+Y = 5 which means Y = 5-X

go to `Z = X - Y` and plug in Y =5-X and simplify

Z = X - Y
Z = X - (5-X)
Z = X - 5 + X
Z = 2X - 5

and that's all there is to it

Answer 10

Is that what they want?

Answer 11

this questions seems too easy to be true lol

Answer 12

looks like what the question is asking, unless there is some other hidden part

Answer 13

Wish I could give you both a best response, could you please give jim_thompson one too?

Answer 14

of course, just did