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True [87]
3 years ago
14

Suppose that X is a random variable with mean 30 and standard deviation 10. Also suppose that Y is a random variable with mean 2

0 and standard deviation 8. Assume that the correlation between X and Y is 0.4. Find the mean and standard deviation of the random variable Z for each of the following cases. Be sure to show your work. a. Z= 2 + 10X. b. Z = X + Y. c. Z = −5X − 3Y
Mathematics
1 answer:
Bas_tet [7]3 years ago
3 0
Part a: For variable X using z score you have (x-30)/10, replace X for this expression in (a), i mean Z=2+10((x-30)/10) = 2+x-30= put this in the way of z score = (x-18)/1, so the mean is 18 and standard deviation is 1.
Part b: Z=X+Y= (x-30)/10 + (x-20)/8 = solve adding fractions = (18x-440)/80 now divide all the numbers between 18 (because you need to show as z score way) = (x-24.4)/4.4, so the mean is 24.4 and standard deviation is 4.4.
For part c,do the same.
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Here's the rule for working with these things:

There are 3 signs associated with a fraction:
=> the sign of the numerator
=> the sign of the denominator
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-- You can change any 2 of them without changing the value of the fraction.

-- Changing any 1 of them changes the effective sign.
___________________________________

Now, you said the fraction is negative.
So, let's start with the positive fraction, and see the different ways
that we could make it a negative fraction:

=> mark only the numerator negative
=> mark only the denominator negative
=> put parentheses around the fraction, and mark it negative outside

If you do any one of these things to a normal positive fraction,
it turns into a negative fraction.

Look at the choices you listed in the question:

-- in the numerator only ?  Yes.  That makes it a negative fraction.

-- in the denominator only ?  Yes. That makes it a negative fraction.

-- both ?  No.  That makes it the same as a positive fraction. 

-- put parentheses around the fraction, and a negative sign outside ?
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-- it doesn't matter ?   No.  I hope you can see that it does matter.

Have I confused you ?
Is this more than you wanted to know ?
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