Question

I'd like to have 30 random numbers generated which are distributed

a) exponentially

b) uniform

c) normal

d) binomial

e) Poisson

Would you please generate 30 random numbers regarding these distributions above, please?

Mean=3

Variance is 2

Answer 1

Note:

1. I have generated the random numbers using R. I am posting the following random nos. with Mean = 3 and Variance = 2.
2. Also, Poisson Distribution has mean = variance, so I have generated 30 poisson variates using mean = 3

Exponential Variates: Mean = 3 and Rate (lambda) = 1/3

6.12405091 1.56378689 0.58907049 3.72425456 0.53281157 5.40521743 1.22549739 0.78002833
1.44778654 4.00271708 0.12015778 0.31206877 0.16223254 5.08650530 0.47559074 2.14431983
0.03888910 0.78374765 1.90625097 1.85884847 2.27775082 0.07041744 2.87155559 0.32581550
0.52401560 3.24002486 1.31517530 1.58642555 1.51100128 6.23794154

Uniform Variates: Mean = 3 and Variance = 2 implies a = 0.5505 and b = 5.4495

3.9799577 1.3469375 2.6235133 2.3269012 2.7647163 1.3105756 3.5081283 2.6333551 4.6484019
4.1205721 3.6214546 5.1009984 0.6282884 4.9423345 3.5407816 4.0720791 1.6734096 2.3817502
2.8462531 2.4227601 4.9195090 2.6131532 1.9795015 5.2851279 1.6162147 2.0669622 1.6775543
4.1111315 3.6982137 2.0835242

Normal Variates: Mean = 3 and Variance = 2

0.30097653 1.39755639 3.67844996 1.94967500 2.80540596 2.45670503 6.08157267
2.91324234 4.90851393 2.29575358 2.37598274 4.58994742 4.00319100 2.89266819
1.92703111 4.17427228 3.38824334 2.30138067 2.77183187 3.40041563 2.60020459
2.77649700 0.39505529 -0.08442628 1.80187258 4.52287469 2.10877891 4.01711749
3.23014636 4.91806523

Binomial Variates: Mean =3 and Variance = 2 implies n = 9 and p = (1/3)

3 1 4 3 5 5 1 2 3 3 3 2 2 3 4 2 4 3 0 2 7 4 1 4 3 2 3 3 2 4

Poisson Variates: Mean = Variance = 3 ( I have taken this)

1 2 5 2 6 0 4 2 4 0 2 4 1 3 1 4 3 5 1 3 2 3 1 0 3 3 5 3 1 1

R- Code: