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Semenov [28]
2 years ago
15

Suppose that – in any given time period – a certain stock is equally likely to go up 1 unit or down 1 unit, and that the outcome

s of different periods are independent. Let X be the amount the stock goes up (either 1 or −1) in the first period, and let Y be the cumulative amount it goes up in the first three periods. Find the correlation between X and Y.
Mathematics
1 answer:
Scorpion4ik [409]2 years ago
3 0

Answer:

Step-by-step explanation:

From the given information:

Let X represent the amount of the stock that goes up in the first period; &

Let Y denote the cumulative amount that goes up in the first three periods.

Then,

X= X_1 + X_2 \\ \\ \\EX=  EX_1 +EX_2\\ \\\\Now ; EX = 0 \\ \\ EX = \dfrac{1}{2}\times 1 + \dfrac{1}{2}\times -1 \\ \\ EX = \dfrac{1}{2}-\dfrac{1}{2} \\ \\ EX = 0

Cov(x,y) = Var(X_1) +Var(X_2) \\ \\ =\dfrac{1}{2}(1+1) + \dfrac{1}{2}(1+1) \\ \\ = \dfrac{1}{2}(2)+ \dfrac{1}{2}(2)  \\ \\ = 1+1  \\ \\ =2

Var (X) = Var (X_1+X_2)\\ \\ = 2 \ Var(X_1)  \\ \\ = 2 \times (1) \\ \\  = 2

Var (Y) = Var (X_1 +X_2+X_3) \\ \\ = 3 \times Var(X_1) = \\ \\ = 3 \times 1\\   \\ = 3

∴

Corr(x,y) = \dfrac{2}{\sqrt{6}} \\ \\ = \dfrac{2}{\sqrt{2\times 3}} \\ \\= \sqrt{\dfrac{2}{3}}

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3(6g+2) -5g

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Answer:

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Step-by-step explanation:

1st week = $439.50

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6 0
3 years ago
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Now factor both terms.

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3 years ago
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Step-by-step explanation:

5 0
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