Mathee: Is the solution correct?
First, I calculated the probabilities and then the expected value. I got the expected value of 3. Is this correct? What should I do now? Thanks!
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There are 8 options for three coin designs.
3x head: 1 possibility with p1 = 1/8
2x head: 3 options with p2 = 3/8
1x head: 3 options with p3 = 3/8
0x head: 1 possibility with p4 = 1/8
Be X the number of head at 3 litters:
E(X) = μ = 3*p1 + 2*p2 + 1*p3 + 0*p4 = 1.5
Var(X) = (3-μ)2*p1 + (2-μ)2*p2 + (1-μ)2*p3 + (0-μ)2*p4 = 0.75
Standard deviation = sqrt(0.75)
Presumption for n litters :
E(X)= n/2
Var(X) = n/4
read again the task, that is, thou shalt “Number of head” (and not “3 times head”) and this has the possible results {0,1,2,3}