Chapter 6 Discrete Random Variables(Probability)

[gmoreno929]

You and a friend are betting on the roll of a die. Specifically you will lose $1 if you roll a 1, 2, or 3, you
will lose $2 if you roll a 4 or 5, and you will win $8 if you roll a 6. Let the random variable X denote the amount of
money you win when playing
this game once.

A)
Find the probability distribution of X.
B)
Find the expected value, standard deviation and variance of X
C)
Explain the meaning of the expected value you obtained in part (b)
D)
Is this a good bet for you? Or for your
friend?

 

[pka]

You and a friend are betting on the roll of a die. Specifically you will lose $1 if you roll a 1, 2, or 3, you
will lose $2 if you roll a 4 or 5, and you will win $8 if you roll a 6. Let the random variable X denote the amount of
money you win when playing
this game once.
A)
Find the probability distribution of X.
B)
Find the expected value, standard deviation and variance of X
C)
Explain the meaning of the expected value you obtained in part (b)
D)
Is this a good bet for you? Or for your friend?

For expected value is the sum of the terms: \(\displaystyle X\cdot\mathscr{P}(X)\)
\(\displaystyle (-1)\mathscr{P}(X=-1)+(-2)\mathscr{P}(X=-2)+(8)\mathscr{P}(X=8)=~?\)

 

[Steven G]

The rules of the forum is that you need to show your work so that we can help YOU solve the problem. Can we see your attempt at doing this problem???

 

[HallsofIvy]

First what is the probability of rolling each of 1, 2, 3, 4, 5, or 6? From that, what is the probability of rolling 1, 2 or 3? Of rolling 4 or 5?