- #1

Mogarrr

- 120

- 6

## Homework Statement

A cohort of hemophiliacs is followed to elicit information on the distribution of time to onset of

AIDS following seroconversion (referred to as latency time). All patients who seroconvert become

symptomatic within 10 years, according to the distribution in Table 6.11.

Table 6.11 Latency time to AIDS among hemophiliacs who become HIV positive

Latency time (years) Number of patients

__Latency Time(years)__:

__Number of patients__

0: 2

1: 6

2: 9

3: 33

4: 49

5: 66

6: 52

7: 37

8: 18

9: 11

10: 4

(I don't know how to make a proper table with latex... tried \being{tabular}{l r} but this doesn't work)

6.64 Assuming an underlying normal distribution, compute 95% CIs for the mean and variance of

the latency times.

## Homework Equations

When the variance is unknown, the t-distribution may be used

[tex] \mu = \bar{x} \pm t_{n,1- \frac {\alpha}2} \cdot \frac {s}{\sqrt {n}} [/tex]

and estimating the variance, we have...

[itex] (n-1) \cdot \frac {s^2}{ \chi^2_{n-1,1- \frac {\alpha}2}} \leq \sigma^2 \leq (n-1) \cdot \frac {s^2}{ \chi^2_{n-1,\frac {\alpha}2}} [/itex]

lastly, for the poisson distribution the confidence interval is given by [itex] \mu_1, \mu_2 [/itex], that satisfies

[itex] \frac {\alpha}2 = P(X \geq \mu | \mu = \mu_1) = \sum_{k=x}^{\infty} \frac {e^{-\mu_1} \mu_1^{k}}{k!}[/itex]

[itex] \frac {\alpha}2 = P(X \leq \mu | \mu = \mu_2) = \sum_{k=0}^{x} \frac {e^{-\mu_2} \mu_2^{k}}{k!}[/itex]

## The Attempt at a Solution

I'm not really sure how to handle this. I'm used to just once column where I can compute the mean and sample variance. Here I'm asked to compute the mean and variance of the

*latency time*. Since this is a time interval, I think I should be using the Poisson distribution, however it's given that the distribution is normal.

I don't know how to proceed. Any help would be appreciated.