A discrete random variable $X$ has the probability distribution: $P(X=x) = kx$ for $x = 1, 2, 3, 4$. Find the value of $k$.
A$\frac{1}{4}$
B$\frac{1}{10}$CORRECT
C$\frac{1}{5}$
D$\frac{1}{8}$
GCEFurther MathematicsProbability and Statistics2022
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Why the answer is B, and why the others tempt you.
Since the sum of all probabilities must equal 1, k(1) + k(2) + k(3) + k(4) = 1, giving 10k = 1, so k = 1/10. Distractors arise from errors such as summing only some values or setting the product rather than sum equal to 1.
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