The random variable X has probability distribution given in the table below - Edexcel - A-Level Maths Statistics - Question 3 - 2008 - Paper 2

To find the values of p and q, we first note that the sum of all probabilities must equal 1:

$p + q + 0.2 + 0.15 + 0.15 = 1$

This simplifies to:

$p + q + 0.5 = 1$

Thus, we can express this as:

$p + q = 0.5$ \quad \text{(1)}

Next, we can use the expected value equation given by:

$E(X) = ext{sum}(x imes P(X=x))$

So we calculate:

$E(X) = (-1)p + 0(q) + 1(0.2) + 2(0.15) + 3(0.15)$

This simplifies to:

$E(X) = -p + 0 + 0.2 + 0.3 + 0.45 = -p + 0.95$

Setting this equal to the given expected value:

$-p + 0.95 = 0.55$

We can rearrange this to find p:

$-p = 0.55 - 0.95$ $-p = -0.4$

Thus:

$p = 0.4$

Using equation (1) to find q, we substitute p into the equation:

$0.4 + q = 0.5$ $q = 0.5 - 0.4$

So:

$q = 0.1$