? 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

2 Answers

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  • cidyah
    Lv 7
    8 years ago
    Favorite Answer

    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)

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  • 3 years ago

    The 4 assumptions (or residences) are a million. basically 2 obtainable consequences. 2. the prospect of success is an identical for each trial. 3. There are n trials, the placement n is continuing. 4. The n trials are self preserving

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