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Random Variables, Expectation & Variance · Question 21 of 68

Question 21

MediumOriginal question

P(X=x)=kxP(X = x) = kx for x=1,2,3,4x = 1, 2, 3, 4, and 0 otherwise. What is P(X≥3)P(X \ge 3)?

Options for question 21

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. k(1+2+3+4)=10k=1k(1 + 2 + 3 + 4) = 10k = 1, so k=110k = \frac{1}{10}.

  2. P(X≥3)=P(3)+P(4)=310+410=710P(X \ge 3) = P(3) + P(4) = \frac{3}{10} + \frac{4}{10} = \frac{7}{10}.

Worth noting

310\frac{3}{10} is P(X=3)P(X = 3) alone; 'at least 3' takes in 4 as well.

Concept
The probability of a range of values
Typical time
90 s
Your time
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The rule this testsProbability distributions
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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.