The score when a spinner is spun is given by the discrete random variable X with the following probability distribution, where a and b are probabilities - Edexcel - A-Level Maths Statistics - Question 5 - 2018 - Paper 1

From the probability distribution, we know that: $a + b = 1$

This provides our first linear equation.

From the first equation, rearranging gives: $b = 1 - a$

Substituting this into the earlier equation $-b + 7a = 2$ yields: $-(1 - a) + 7a = 2$

This simplifies to: $8a - 1 = 2$ Thus, we have: $8a = 3 \Rightarrow a = 0.375$

Using our first equation:

1. From $a + b = 1$, with $a = 0.375$, we substitute to find: $b = 1 - 0.375 = 0.625$

We have the transformation for Y as: $Y = 10 - 3X$

Thus, using the formula for the expectation: $E(Y) = 10 - 3E(X) = 10 - 3 imes 2 = 4$

Using the variance transformation property: $Var(Y) = 9 imes Var(X)$ Substituting Var(X) = 7.1: $Var(Y) = 9 imes 7.1 = 63.9$

To find P(Y > X): We first analyze the relationship between Y and X separately. Given that: Y can take values {$10 - 3x$} when X takes values {±1, 0, 2, 4, 5}. This means evaluating P for each combination of X and Y, ultimately leading to: $P(Y > X) = P(Y = 0) + P(Y = 1) + P(Y = 2) + P(Y = 3) = 0.55$