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Random Variables, Expectation & Variance · Question 25 of 68

How many cars does the showroom expect to sell a day?

Question 25

MediumOriginal 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.

How many cars does the showroom expect to sell a day?

Options for question 25

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. E(X)=0(0.1)+1(0.2)+2(0.3)+3(0.2)+4(0.2)E(X) = 0(0.1) + 1(0.2) + 2(0.3) + 3(0.2) + 4(0.2).

  2. 0+0.2+0.6+0.6+0.8=2.20 + 0.2 + 0.6 + 0.6 + 0.8 = 2.2.

Worth noting

2 is the middle value of 0 to 4; the weights pull the mean above it.

Concept
Expectation as a weighted mean
Typical time
120 s
Your time
—
The rule this testsProbability distributions
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