Dear student, we can solve one question at a time, please help to upload other questions separately. Here, I am answering question 2.
X | P(X) | X**2 | (X**2)*P |
1 | 0.25 | 1 | 0.25 |
2 | 0.05 | 4 | 0.2 |
3 | 0.15 | 9 | 1.35 |
4 | 0.15 | 16 | 2.4 |
5 | 0.1 | 25 | 2.5 |
6 | 0.3 | 36 | 10.8 |
Sum | 17.5 |
Expected E(X) = ΣX*P(X) = 1*0.25 + 2*0.05 + 3*0.15 + 4*0.15 + 5*0.1 + 6*0.3 = 3.7
E(X) = 3.7
Var(X) = Σx2p − μ2
Var(X) = 17.5 - 3.7**2 = 17.5 - 13.69 = 3.81
Var(X) = 3.81
Fill in the P(X = x) values to give a legitimate probability distribution for the discrete...
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