Hi Expert please help me with the following questions:

{Discussion 1}

applications of the exponential probability distribution

1) please give an example of real life applications of the exponential probability distribution

2) please describe the application.

3) Use R to generate a plot of the exponential distribution and use parameters that would be relevant to the application. Please STATE the parameters used and show the plot here

4) Interpret the plot.

{Discussion 2}

examine the following transition matrix and state names below. Both the image and state names are taken from a real-life study report on infectious diseases

Probability Transition Matrix for a 5 -State Markov Matrix Row and column names Infectious Disease Process 0. 93 0.07 0.00 0.00 0.00 (1); Non-Infected population 0. 05 0.80 0.10 0.05 0.00 (2): Infected (isolated at home or hospital) 0.00 0.15 0.80 0.05 0.00 (3): Hospitalized (after becoming ill); 0.00 0.00 0.05 0.80 0.15 (4): In the hospital ICU (or ventilators); 0.00 0.00 0.00 0.00 1.00 (5) Dead (absorbing state; no return)