**Poisson Random Variable **

**True or false. If false, indicate what should be changed to make true.**

1, Prevalence may be modeled as a Poisson random variable.

2, A cohort study should always be conducted whenever it may be possible.

3, A normal distribution may be bimodal.

4, Results from studies should always be generalized to the entire population regardless of the sample.

5, A confidence interval will always contain the true value of the population parameter.

6, If X ~ B (10, 0.1), then 5 successes are as likely as 5 failures.** **

**Solution**** **

- Q: Prevalence may be modelled as a Poisson random variable.

A: **True.** The event parameter **λ**can be taken as the prevalence rate.

- Q: A cohort study should always be conducted whenever it may be possible.

A: There are two possible scenarios.

**True: **If cost is not a factor, hence we can perform it on the whole population, and if the design is for a very specific and rare case then cohort study should be conducted. Depends on the context.** **

**False:** This is because of lack of randomization (imbalances in patient characteristics could exist), and the fact that outcome of interest may take some time to occur, hence very expensive.

Hence if the design is not for rare diseases, it’s better to use case-control study,

- Q: A normal distribution may be bimodal.

A: **False.** A normal distribution is always unimodal will be true.

- Q: Results from studies should always be generalized to the entire population regardless of the sample.

A: **False.**The sample on which the studies have been conducted may not be representative of the population from which it has been taken.

So “Results from studies should **not** always be generalized to the entire population regardless of the sample” will be true.

- Q: A confidence interval will always contain the true value of the population parameter.

A: **False. **An X % confidence interval means that we are X% confident that the true population parameter is between the lower and upper calculated values. Hence for a 95% (for example) confidence interval, we cannot say for certain that the true value lies in the interval.

“A confidence interval might not contain the true value of the population parameter” will be true.

- Q: If X~B(10,0.1) then 5 successes are as likely as 5 failures.

A: **True. **Probability of 5 successes in 10 trials means 5 successes and 5 failures, which also means 5 failures. Hence 5 successes are as likely as 5 failures.