9709 · topic questions
Continuous random variables
12 past-paper questions on Continuous random variables
Show that E(X) = 1/2 - 2/π².
Show that E(X) = 8/(3√π).
It is given that E(X) = ln 3. (c) Show that b = 2 and find the value of a.
Find the exact value of E(X).
X is a random variable with probability density function given by f(x) = { (1/π)(1+cosπx) for 0 ≤ x ≤ 1, 0 otherwise. (a) Show…
Find the median of X.
The probability density function, f, of a random variable X is given by f(x) = k(1+cosx) for 0 ≤ x ≤ π, and 0 otherwise, where k…
A random variable X has probability density function f defined by f(x) = { a/x² - 18/x³ for 2 ≤ x ≤ 3, 0 otherwise, where a is a…
Show that E(X) = 27/2 ln(3/2) - 3.
Find the median of X.
Verify that the median of X lies between 0.83 and 0.84.
The random variable X has probability density function given by f(x) = kx²/a² for 0 ≤ x ≤ a, 0 otherwise, where k and a are…
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Continuous random variables (9709) past-paper questions — marked instantly
These are real Cambridge Mathematics past-paper questions on Continuous random variables. Open one, attempt it, then upload your working — MarkScheme grades it against the official 9709 mark scheme so you see exactly where the marks are won and lost on this topic.
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