BitWithBite
Mathematics Worksheet
📉 Probability Distributions
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After this worksheet you can
Check whether a distribution is valid.Ensure probabilities lie between 0 and 1.Compute a cumulative probability F(x).Distinguish a PMF from a PDF.📚 Quick Recap
A probability distribution describes how probabilities are spread across all the possible values of a random variable — the complete 'shape' of randomness for that variable.
🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1Is P(X=0)=0.1, P(X=1)=0.4, P(X=2)=0.5 a valid distribution?
2Is P(X=0)=0.2, P(X=1)=0.3, P(X=2)=0.3 valid?
3For P(X=0)=0.1, P(X=1)=0.4, P(X=2)=0.5, F(1) =:
4Using the same distribution, F(2) =:
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5A valid distribution's probabilities sum to .
6Each probability must lie between 0 and .
7Is P(X=0)=0.1, P(X=1)=0.4, P(X=2)=0.5 a valid distribution?
8Is P(X=0)=0.2, P(X=1)=0.3, P(X=2)=0.3 valid?
9For P(X=0)=0.1, P(X=1)=0.4, P(X=2)=0.5, find F(1).
🚀 Section C · Challenge ● CHALLENGE 5
10Using the same distribution, find F(2).
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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✂ answer key — fold or cut before handing out
1-A 2-B 3-A 4-A | 5 1 6 1 7 = Yes, sums to 1 8 = No, sums to 0.8 9 = 0.5 | 10 = 1.0