? asked in Science & MathematicsMathematics · 8 years ago

Probability Mass Function?

A box contains 12 marbles. Six of the marbles are red, four are green, and two are yellow. Suppose that you choose three marbles at random. let x be the number of red marbles in the sample, y be the number of green marbles, and z be the number of yellow marbles.

a. Give the precise formulas for the probability mass functions of the three random variables, f(x), f(y), and f(z).

b. Suppose you win \$1 for each green marble in your sample and lose \$1 for each red marble (yellow has no financial consequences). Let w be your net winnings or losses. Construct the P.M.F of w as a table. (obviously the table part cannot be shown in this answer)

c. Find the expected value of w and explain its significance.

d. Find the standard deviation of w.

Any help would be great and if you can explain that would be even better. Please and thank you

Relevance
• cidyah
Lv 7
8 years ago

a)

Let x be the number of red marbles.

3 marbles out of 12 may be drawn in C(12,3) ways.

x,y, and z have discrete distributions.

Probability distribution of x:

f(x) = P(x = k) = C(6,k) C(6,3-k) / C(12,3) , k=0,1,2,3 -----(1)

Probability distribution of y:

f(y)= P( y=k ) = C(4,k) C(8,3-k) /C(12,3) , k=0,1,2,3 ------(2)

Probability distribution of z :

f(z)= P( z = k) = C(2,k) C(10,3-k) /C(12,3) , k=0,1,2 -----(3)

b)

w-------------p(w)

0 ------------P(x=0)+P(y=0)+P(z=0)+P(z=1)+P(z=2)

-1 -----------P(x=1)

-2 -----------P(x=2)

-3 -----------P(x=3)

1-------------P(y=1)

2 ------------P(y=2)

3 ------------P(y=3)

You have to evaluate the probabilities above to get the probability distribution of w.

Then, you may answer (c) and (d)