Answer:
a)
b)
Step-by-step explanation:
Part a
We assume that the parachutist lands at random point in the interval (x=A,y=B) we have a continuous random variable X. And the distribution of X would be uniform . And the density function would be given by:
And 0 for other case.
The operation fails, if parachutist's distance to A is more than five times as much as her distance to B.
So the point P in the interval (A,B) at which the distance to A is exactly 5 times the distance to B is given by:
And we can find the probability desired like this:
And from the cumulative distribution function of X ficen by we got:
Part b
For this case we assume that
On this case we assume that
The density function for the Gamma distribution is given by:
And on this case we can find the probability using the complement rule like this:
We can solve this problem with the following excel code:
"=1-GAMMA.DIST(1;2;1;TRUE)"
And if we do it by hand we need to do this: