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Random Variables, Expectation & Variance · Question 13 of 68

What is the variance of the number of tails in the four tosses?

Question 13

MediumOriginal question

Four fair coins are tossed together, and XX is the number of tails that show.

What is the variance of the number of tails in the four tosses?

Options for question 13

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. E(X)=2E(X) = 2, and E(X2)=0+4+24+36+1616=5E(X^{2}) = \frac{0 + 4 + 24 + 36 + 16}{16} = 5.

  2. Var(X)=5−22=1\text{Var}(X) = 5 - 2^{2} = 1.

Worth noting

5 is E(X2)E(X^{2}); the variance takes away 222^{2}.

Concept
Variance from the distribution
Typical time
120 s
Your time
—
The rule this testsRandom variables
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Ten questions from Random Variables, Expectation & Variance, at your own pace.

Practise this chapter →

Ten questions from Random Variables, Expectation & Variance, at your own pace.