- #1

JasonBrewer

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## Homework Statement

1. Assume each birth in a hospital on a given day is independent of one another, and each birth, P(boy)=0.48. What is the probability that the 8th baby born is the 5th girl.

2. Two random variables X and Y have joint distribution given by. What is their correlation.

3. Z is drawn randomly from {1,2,3,4,5}. Independently of Z, 4 other RVs Y1,...,Y4 are drawn randomly, with replacement, from {1,...,6}. Define X as the number of Yjs less than or equal to Z. What is the variance of X?

## Homework Equations

2. Corr(X,Y)=Cov(X,Y)/((Var(X),Var(Y)^0.5)

where Cov(X,Y)=E(X,Y)-E(X)E(Y)

## The Attempt at a Solution

I think that most of my problem comes from not being able to apply the formulas and theory since my teacher doesn't do very many problems, and mainly does proofs which I don't find too helpful.

Anyways my theory.

1. So I think that I need to find the probability that out of the first 7 babies, 4 are girls, and I'm almost certain that this is a binomial. But from there, I don't know what to do. Then multiply by the chance that the 8th born, is a girl (0.52).

Edit: I got this one! I found the forumla for probability and applied it.

2. This is an issue what I don't know how to intepret the data. To find Var, I need to Expectation, but how do I find it? Which numbers do I multiple to get it.

I also need to find Cov(X,Y) which require E(X,Y), which I am also clueless to find when the data is in this form.

Is it E(X)=-1*(0.1+0.1+0.1)+0(0.1+0.15+0.1)+1(0.15+0.1+0.1)

and E(Y)=-1(0.35)+1(0.3)

When I tried this, the answer was almost certainly incorrect, since I got a positive answer, and the real answer I know is -ve.

I thought that maybe the above might be correct, and I just don't know how to compute E(X,Y) correctly.

3. This last one, I was given a hint. Var(X)=var[4z/5]+E((4z/5)(1-(z/5))

I still don't know how to do this question even with this forumla. I assume that there are only a couple more steps (2?), but I don't know how to continue with the question.

Thanks for any help

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