The below table data for party size and revenue per person is stored in an Excel file.

party_size	rev_per_person
17	151.79
23	159.09
22	213.09
22	150.5
15	132.59
24	223.29
23	182.24
21	207.42
17	139.91
19	208.9
25	274
20	265.19
23	201.04
23	227.19
19	228.67
18	158.53
20	127.18
23	158.56
18	145.03
26	218.6
21	197.85
18	134.63
18	144.27
17	118.26
20	167.43
22	170.97
18	107.51
21	209.37
24	293.59
16	150.69
16	145.02
27	255.66
21	190.96
21	286.94
21	267.34
15	152.41
19	190.51
20	178.01
16	186.86
22	133.5
23	171.16
27	190.02
25	273.13
23	212.53
18	153.95
15	162.79
18	130.91
16	190.36
14	238.77
20	167.61
17	168.93
17	152.82
19	104.29
23	212.42
21	183.89
24	210.14
16	123.93
19	105.4
20	137.27
19	165.63
14	91.92
16	168.79
21	204.62
22	127.9
27	184.54
21	155.23
15	181.05
20	116.86
20	193
21	242.41
17	173.8
15	132.23
18	146.84
21	190.19
15	139.6
19	149.98
22	193.36
21	124.13
18	174.41
23	183.8
22	167.32
21	133
16	136.2
18	173
16	129.23
19	167.46
21	182.66
24	165.83
22	112.78
18	177.66
17	97.91
24	169.8
19	201.27
13	81.42
22	227.41
18	141.74
24	198.4
17	157.16
21	199.25
21	150.07

(set a seed of 123 to perform below in R Studio)

The correlation between party_size and rev_per_person is 0.5068473.

a. Using Poisson distribution for party_size (lambda <- 19.84) and gamma distribution (shape = 15.9386656 and scale = 10.88882) for rev_per_person and the correlation of 0.5068473., construct an MC simulation with 100,000 trials to create a risk profile for the revenue generated from a single event. Develop a histogram and provide the mean and standard deviation.

b. According to your simulation, how often will a private function generate at least $5000?

c. Repeat parts (a) and (b), and build a simulation that ignores the correlation. How does this affect your results?