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Random Variables, Expectation & Variance · Question 28 of 68

What is the variance of the showroom's daily sales?

Question 28

HardOriginal question

A car showroom sells XX cars a day, where XX takes the values 0, 1, 2, 3 and 4 with probabilities kk, 2k2k, 3k3k, 2k2k and 2k2k.

What is the variance of the showroom's daily sales?

Options for question 28

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. E(X2)=0+0.2+1.2+1.8+3.2=6.4E(X^{2}) = 0 + 0.2 + 1.2 + 1.8 + 3.2 = 6.4.

  2. Var(X)=6.4−2.22=6.4−4.84=1.56\text{Var}(X) = 6.4 - 2.2^{2} = 6.4 - 4.84 = 1.56.

Worth noting

6.4 is E(X2)E(X^{2}) before the square of the mean is taken away.

Concept
Variance = E(X²) − [E(X)]²
Typical time
150 s
Your time
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The rule this testsProbability distributions
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