Answer:
The distribution is
Solution:
As per the question:
Total no. of riders = n
Now, suppose the is the time between the departure of the rider i - 1 and i from the cable car.
where
= independent exponential random variable whose rate is
The general form is given by:
(a) Now, the time distribution of the last rider is given as the sum total of the time of each rider:
Now, the sum of the exponential random variable with with rate
is given by:
Answer:
3, in both a), b)
Step-by-step explanation:
a) The slope of the line tangent to the curve that passes through the point (2,-10) is equal to the derivative of p at x=2.
Using differentiation rules (power rule and sum rule), the derivative of p(x) for any x is . In particular, the value we are looking for is
.
If you would like to compute the equation of the tangent line, we can use the point-slope equation to get
b) The instantaneus rate of change is also equal to the derivative of P at the point x=2, that is, P'(2). This is equal to .