WJEC Statistics 1 - Key Facts

What does it mean if events A and B are mutually exclusive?

Also, \(P(A\cap B)=?\)

What does it mean if events A and B are independent?

Also, \(P(A\cap B)=?\)

\[P(A|B)=?\] (there is a rearranged version of this given in the formulae book)

If events A and B are independent, then \(P(A|B)=?\)

If events A and B are independent, then \(P(B|A)=?\)

The addition law for events A and B is \[P(A\cup B)=?\] (given in formulae book)

\[P(A')=?\]

For events A and B that are NOT independent, \[P(A\cap B)=?\]

What is a sample space?

How many unordered samples of size \(r\) can be taken from a collection of \(n\) objects?

For any discrete random variable \(X\),\[\text{E}(aX + b) = ?\]

For any discrete random variable \(X\),\[\text{Var}(aX + b) = ?\]

For a discrete random variable \(X\) taking values \(x_i\) with probabilities \(p_i\), \[\text{E}(X)=?\] (given in formulae book)

For a discrete random variable \(X\) taking values \(x_i\) with probabilities \(p_i\), \[\text{Var}(X)=?\] (given in formulae book)

Give the formula for the expected value of a function \(g(X)\) of a discrete random variable

(given in formulae book)

\[X \sim B(n,p)\] \(\text{E}(X)=?\)
(given in formulae book)

\[X \sim B(n,p)\] \(\text{Var}(X)=?\)
(given in formulae book)

\[X \sim Po(\lambda)\] \(\text{E}(X)=?\)
(given in formulae book)

\[X \sim Po(\lambda)\] \(\text{Var}(X)=?\)
(given in formulae book)

How would you use the Binomial or Poisson tables to find \(P(X=n)\)?

How would you use the Binomial or Poisson tables to find \(P(X>n)\)?

How would you use the Binomial or Poisson tables to find \(P(X\geq n)\)?

How would you use the Binomial or Poisson tables to find \(P(X<n)\)?

For a continuous probability distribution, how are \(f(x)\) and \(F(x)\) related?

If \(q\) is the lower quartile of a continuous random variable \(X\) with cumulative distribution function \(F\), then \[F(q)=?\]

If \(m\) is the median of a continuous random variable \(X\) with cumulative distribution function \(F\), then \[F(m)=?\]

If \(Q\) is the upper quartile of a continuous random variable \(X\) with cumulative distribution function \(F\), then \[F(Q)=?\]

Give the formula for the expected value of a function \(g(X)\) of a continuous random variable

(given in formulae book)

For a binomial distribution \(X\sim B(n,p)\), what is the formula for \(P(X=x)\)?

(given in formulae book)

For a Poisson distribution \(X\sim Po(\lambda)\), what is the formula for \(P(X=x)\)?

(given in formulae book)

How is variance related to standard deviation?

\[X\sim B(n,p)\]
What values can \(X\) take?

\[X\sim Po(\lambda)\]
What values can \(X\) take?