Write a single MATLAB function called calcProbs which can do each of the following three tasks.

Note: A single function, with appropriate inputs and outputs as described in the questions below, is required. You should only submit your answer after you have done each of the three parts below.

Part $1$: Understanding of Basic Probability Concepts $(20\%)$

Your function should be able to take in a probability density function called pdf and an interval $[$a$,$ b$]$ and return a variable, prob, which is the probability of a random variable falling within that interval.

Note: You should not define a specific pdf$,$ but allow the function to work for an arbitrary pdf$.$

Part $2$: Working with the Normal Distribution $(40\%)$

Leaving the previous inputs and outputs for the previous part, add additional inputs to accept the parameters mu$1($mean$)$ and sigma$1($standard deviation$)$ for a normal distribution. The function should plot, with x and y labels, the PDF of the distribution and update it to also return the values

mean$\_$val, one$\_$std$,$ two$\_$std

at which the normal PDF is at its mean, one standard deviation away, and two standard deviations away

Part $3$: Application of Probability Distributions $(40\%)$

Finally, update your function to take two further normal distribution parameters, mu$2($mean$)$ and sigma$2($standard deviation$)$ and output the variable area which calculates the area of overlap between the two distributions.