## January 18, 2007

## January 13, 2007

### Statistics 2 Test (for myself)

This test mainly tests the qualitative bits of the S2 exam. I am more confident on the quantitative parts.

**Question 1**

State clearly the conditions under which it is appropriate to assume that a random variable has a

(a) binomial distribution (3)

(b) Poisson distribution (3)

**Question 2**

State the circumstances under which:

(a) a Poisson distribution may be used as an approximation to a binomial distribution (2)

(b) a normal distribution may be used as an approximation to a binomial distribution (3)

(c) a normal distribution may be used as an approximation to a Poisson distribution (1)

**Question 3**

The continuous uniform distribution has probability density function, f(x) = 1/(b – a) for a to b, and 0 otherwise. Derive:

(a) its mean (5)

(b) its variance (8)

(c) its cumulative distribution function (3)

**Question 4**

Define:

(a) population (1)

(b) census (2)

(c) sample (2)

(d) sampling unit (1)

(e) sampling frame (2)

(f) statistic (2)

(g) sampling distribution (2)

(h) hypothesis testing (3)

END!