Probability Density Function (Edexcel A-Level Further Mathematics): Quizzes

📚Quizzes
Revision NotesModel AnswersQuizzesFlashcardsExam Questions
Probability Density Function
Sign up to keep practising.Create a free account to play more quizzes and track your progress.

Practise the questions

10 questions from this quiz

Show

What must ∫−∞∞f(x) dx\int_{-\infty}^{\infty} f(x) \, dx equal for f(x)f(x) to be a valid PDF?

11

Which condition must f(x)f(x) satisfy for all xx to be a valid PDF?

f(x)≥0f(x) \geq 0

Why is f(x)=14xf(x) = \frac{1}{4}x for −1≤x≤2-1 \leq x \leq 2 not a valid PDF?

f(x)f(x) becomes negative

If ∫13f(x) dx=823\int_1^3 f(x) \, dx = 8\frac{2}{3}, why is f(x)f(x) not a valid PDF?

Total integral ≠1\neq 1

Given ∫14kx3 dx=1\int_1^4 kx^3 \, dx = 1, what value of kk makes this a valid PDF?

4255\frac{4}{255}

For continuous random variable XX, what is P(X=k)P(X = k)?

00

If f(x)f(x) is a PDF, what does the CDF F(x)F(x) represent?

P(X≤x)P(X \leq x)

For a PDF with domain [a,b][a, b], what is F(b)F(b)?

11

How do you find the PDF f(x)f(x) from the CDF F(x)F(x)?

f(x)=ddxF(x)f(x) = \frac{d}{dx}F(x)

What indicates a positively skewed PDF?

Mode < Median or Mean

Explore Edexcel A-Level Further Mathematics Revision Notes by Topics

Discrete Probability Distributions

Explore Edexcel A-Level Further Mathematics Model Answers by Topics

Discrete Probability Distributions

Explore Edexcel A-Level Further Mathematics Flashcards by Topics

Discrete Probability Distributions

Explore Edexcel A-Level Further Mathematics Exam Questions by Topics

Discrete Probability Distributions

Join 100,000+ A-Level students studying Quizzes with us.

Select your subjects, and get access to A+ resources today.