Question

Consider a group of people who have received treatment for a disease such as cancer. let tt be the survival time, the number of years a person lives after receiving treatment. the density function giving the distribution of tt is p(t)=ce−ctp(t)=ce−ct for some positive constant cc, and the cumulative distribution function is p(t)=∫t0p(x)dxp(t)=∫0tp(x)dx. think carefully about what the practical meaning of p(t)p(t) is, being sure that you can put it into words.

Answer 1

So we are given a distribution:

`p(t)=ce^(-ct)`
Suppose we are looking at the probability that a person in the group live less than d days. Then we will use the integral the following way:

`P(x\ \textless \ d)=\int_(t_0)^dce^(-ct)dt`

Answer 2

Solution :- Let X be a group of people who have received treatment for cancer ,

and t be the survival time(The number of years a person lives after receiving treatment).

Now the density function giving the distribution of t =
`p(t)=ce^(-ct)`

for some positive constant c.

So to know the probability of a person of the given group live not more than d days, the cumulative distribution function is given by

`P(X\leq\ d )=\int\limits^d_(t_0){ce^(-ct)\ dt` where c be any constant.

The distribution function P(t), also called the cumulative distribution function (CDF) , which tells the probability that a variate T takes a value less than or equal to a number t. And P(t)is greater than 0 and less than1