Please explain the reasoning with calculation, thank you!
Question: If we toss a coin n times. x and y are number of heads and tails. What's the correlation coeffcient between x and y?
a)-1 b)0 c)1/2 d)1
Here,
X + Y = n
So,
E(X) + E(Y) = E(n) = n
On subtracting above two equations, we will have:
X - E(X) = - (Y - E(Y))
So,
Cov(X, Y) = E((X - E(X))(Y - E(Y)) = E(-(X - E(X))(X - E(X)) = - Var(X)
Also,
Var(X) = Var(Y)
Therefore,
Option A is correct.
Please explain the reasoning with calculation, thank you! Question: If we toss a coin n times....
please explain so clearly with step by step thank! Example 1.19.2. We toss a coin three times. Let X (Y) be the random variable which gives the number of heads from the first (last) two tosses. Show t 1. E(X) E(Y)-1; 4. has the distribution 1 +Y 0 3 2 3 1+Y 212 1 2
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