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aivan3 [116]
3 years ago
5

Suppose that 3 balls are chosen without replacement from an urn consisting of 5 white and 8 red balls. Let Xi equal 1 if the ith

ball selected is white and let it equal 0 otherwise. Give the joint probability mass function of X1 , X2.

Mathematics
1 answer:
Katarina [22]3 years ago
4 0

Answer:

The joint probability mass function table is provided below.

Step-by-step explanation:

The experiment consist of drawing 3 balls from an urn containing 5 white and 8 red balls.

The random variable <em>Xi</em> is defined as follows:

<em>Xi</em> = 1; if the ith ball is white

<em>Xi</em> = 0; otherwise.

Then <em>X</em>₁ = the 1st ball is white and <em>X</em>₂ = the 2nd ball is white.

The sample space is as follows:

S = {(X₁ = 0, X₂ = 0), (X₁ = 0, X₂ = 1), (X₁ = 1, X₂ = 0), (X₁ = 1, X₂ = 1)}

Compute the probability of each event in the sample space as follows:

P(X_{1} = 0, X_{2}= 0)=\frac{8}{13} \times\frac{7}{12}=\frac{14}{39}

P(X_{1} = 0, X_{2}= 1)=\frac{8}{13} \times\frac{5}{12}=\frac{10}{39}

P(X_{1} = 1, X_{2}= 0)=\frac{5}{13} \times\frac{8}{12}=\frac{10}{39}

P(X_{1} = 1, X_{2}= 1)=\frac{5}{13} \times\frac{4}{12}=\frac{5}{39}

The joint probability mass function table is provided below.

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The explicit rule for the arithmetic sequence shown in the graph is a↓n=9.5+2(n-1)
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True.

Step-by-step explanation:

The explicit form for an arithmetic sequence is:

a_n=a_1+d(n-1)

where a_1 is the first term and d is the common difference.

The common difference here is 2 because the y's are going up by 2 while the x's are going up by 1.

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So the answer is true.

----

You can also verify by plugging in numbers for n and see if you get the outputs mentioned in the pairs given:

Let n=1:

a_1=9.5+2(1-1)

a_1=9.5+2(0)

a_1=9.5+0

a_1=9.5

Let n=2:

a_2=9.5+2(2-1)

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a_3=9.5+4

a_3=13.5

Let n=4:

a_4=9.5+2(4-1)

a_4=9.5+2(3)

a_4=9.5+6

a_4=15.5

Let n=5:

a_5=9.5+2(5-1)

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Let n=6:

a_6=9.5+2(6-1)

a_6=9.5+2(5)

a_6=9.5+10

a_6=19.5

We have confirmed that we get all 6 of the mentioned points using the equation they gave.

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3 years ago
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