S1 June 2014 (R) Q2
2. The discrete random variable \(X\) has probability distribution
\[\mathrm{P}(X = x) = \frac{1}{10} \qquad x = 1, 2, 3, \ldots\ 10\](a) Write down the name given to this distribution. (1)
(b) Write down the value of
(i) \(\mathrm{P}(X = 10)\)
(ii) \(\mathrm{P}(X \lt 10)\) (2)
The continuous random variable \(Y\) has the normal distribution \(\mathrm{N}(10, 2^2)\)
(c) Write down the value of
(i) \(\mathrm{P}(Y = 10)\)
(ii) \(\mathrm{P}(Y \lt 10)\) (2)
| Scheme | Marks |
|---|---|
| (Discrete) Uniform | B1 |
| (1) |
Notes
B1 for seeing the word uniform
Condone “continuous” uniform
| Scheme | Marks |
|---|---|
| (i) \(\mathrm{P}(X = 10) = \dfrac{1}{10}\) | B1 |
| (ii) \(\mathrm{P}(X \lt 10) = \dfrac{9}{10}\) | B1 |
| (2) |
| Scheme | Marks |
|---|---|
| (i) \(\mathrm{P}(Y = 10) = 0\) | B1 |
| (ii) \(\mathrm{P}(Y \lt 10) = \dfrac{1}{2}\) | B1 |
| (2) | |
| (5 marks) |