Mathematics Probability & Statistics 2 9709: Continuous Random Variables Topical Past Paper Questions

The diagram shows the graph of the probability density function, $f(x)$, of a random variable $X$. For $0 \leqslant x \leqslant a$, the graph is a straight line from $O$ to the point $(a, b)$, where $a$ and $b$ are constants. Elsewhere $f(x) = 0$. (a) Show that the median of $X$…

The diagram shows the graph of the probability density function, f, of a random variable X. The graph is a straight line from $ (0, a) $ to $ (b, 0) $ where a and b are constants. Elsewhere $ f(x) = 0 $. (a) Find an expression for $b$ in terms of $a$. (b) Given that $ E(X)=\frac{…

The graph of the probability density function f of a random variable X is symmetrical about the line x = 2. It is given that P(2 -1) = \frac{245}{256} $. It is now given that, for x in a suitable domain, $ f(x) = k(12 + 4x - x^2) $, where $ k $ is a constant. (b) Find the value o…