Edexcel IAL S1 Discrete Random Variables Questions
Probability distributions of discrete random variables, expectation E(X), variance Var(X), cumulative distribution functions.
- S1 · Statistics 1
- Calculator allowed
- 35 practice questions
What the questions test
The 35 S1 discrete random variables practice questions cover:
Worked example 1
A discrete random variable $X$ has $E(X) = 2$ and $Var(X) = 4$. Another variable is defined as $Y = aX + b$, where $a > 0$. Given that $E(Y) = 10$ and $Var(Y) = 36$, find the values of the constants $a$ and $b$.
Mark scheme
- M1 for using the variance property $Var(Y) = a^2 Var(X)$ to write $36 = a^2(4)$.
- A1 for solving to find $a^2 = 9 \implies a = 3$ (since $a > 0$).
- M1 for using the expectation property $E(Y) = aE(X) + b$ to write $10 = a(2) + b$.
- M1 for substituting $a=3$ into the equation: $10 = 3(2) + b$.
- A1 for concluding $b = 4$.
Worked example 2
The discrete random variable $X$ takes the values $1, 2,$ and $3$ with probabilities $a, b,$ and $0.3$ respectively. Given that $E(X) = 1.9$, find the values of $a$ and $b$.
Mark scheme
- M1 for forming the sum of probabilities equation: $a + b + 0.3 = 1 \implies a + b = 0.7$.
- M1 for forming the expected value equation: $1(a) + 2(b) + 3(0.3) = 1.9 \implies a + 2b = 1.0$.
- M1 for solving the simultaneous equations (e.g., subtracting the first from the second: $b = 1.0 - 0.7$).
- A1 for concluding $b = 0.3$ and $a = 0.4$.
FAQ
What discrete random variables is in Edexcel IAL S1?
Probability distributions of discrete random variables, expectation E(X), variance Var(X), cumulative distribution functions.
Is S1 a calculator paper?
Yes, a calculator is allowed in S1, but method marks are only given for working you write down.
How are S1 discrete random variables questions marked?
With M marks for a correct method, A marks for accurate answers that depend on the M mark before them, and B marks for independent results, as in the worked examples on this page.