Statistics I20795 marksNumerical: expectation and varianceMathematical expectation of a random variable
A coin is tossed two times and if X denotes the number of heads obtained, find (i) E(x) (ii) E(x2) (iii) V(x) (iv) E(2X2 + 3x - 5)
A coin is tossed two times and if X denotes the number of heads obtained, find (i) $E(x)$ (ii) $E(x^2)$ (iii) $V(x)$ (iv) $E(2X^2 + 3x - 5)$ [5]
- Fair coin tossed 2 times - X = number of heads - Possible values: X = 0, 1, 2 - Sample space: {TT, HT, TH, HH}, each equally likely with probability 1/4 X Outcomes P(X) ------------------- 0 TT 1/4 1 HT, TH 1/2 2 HH 1/4 Check: $\frac{1}{4}+\frac{1}{2}+\frac{1}{4}=1$ ✓ --- $$E(X)=\sum X\cdot P(X...