Answer:
a) 
b) 
Explanation:
Previous concepts
The cumulative distribution function (CDF) F(x),"describes the probability that a random variableX with a given probability distribution will be found at a value less than or equal to x".
The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution".
Part a
Let X the random variable of interest. We know on this case that 
And we know the probability denisty function for x given by:

In order to find the cdf we need to do the following integral:

Part b
Assuming that
, then the density function is given by:

And for this case we want this probability:

And evaluating the integral we got:

A diagram showing a use case diagrams for these requirements is given in the image attached.
<h3>What is system
Case diagram?</h3>
A use case diagram is known to be a kind of graphical illustration of a users in terms of their various possible association or interactions within any given system.
A use case diagram in banking can be used to prepare, depict and also to know all the functional requirements of the banking system.
Therefore, Give the use case specification for the banking system services and paying a bill online is given in the image attached.
Learn more about Case diagram from
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I think the answer is B. 10D