CMA Foundation · Fundamentals of Business Mathematics and Statistics · Probability
A fair coin is tossed 3 times. Let X be the number of heads. What is E(X) and E(X²)?
E(X) is 1.5 and E(X²) is 3. With probabilities 1/8, 3/8, 3/8 and 1/8 for 0 to 3 heads, the mean is 12/8 and the mean of squares is 24/8. Squaring the mean instead gives 2.25, which is incorrect.
- AE(X)=1.5 and E(X²)=3Correct
- BE(X)=1.5 and E(X²)=2.25
- CE(X)=1.5 and E(X²)=3.5
- DE(X)=1 and E(X²)=3
Explanation
P(X=0,1,2,3) = 1/8, 3/8, 3/8, 1/8. E(X) = (0+3+6+3)/8 = 1.5. E(X²) = (0+3+12+9)/8 = 24/8 = 3. The option 2.25 is just (E X)², which wrongly squares the mean.
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