Probability - Poisson Distribution - Computer Science Assignment Help

Assignment Task:

Question 1
We will start slowly. Simulate rolling 5 fair dice and computing the sum of the 5 rolled numbers. Repeat this 1000 times, and calculate how many times the sum was exactly 6. From this, calculate the probability.

Question 2
The number of cars stopping at a remote rest area in one day is distributed according to a Poisson distribution with mean λ = 3. Find the probability that in a given day, at most one car will stop at the rest area.

Question 3
An urn contains 5 yellow balls, 3 green balls, 7 yellow cubes and 1 red cube. One of these objects is selected at random. Consider the following events:
A = The selected object is a cube.
B = The selected object is yellow.
This one is a bit trickier, since we are selecting two variables (shape and color) at the same time. There are number of ways to do this. If you want to figure out your own way, please do. I personally recommend using the capabilities of the tibble package. One advantage is that since tibble is a part of the tidyverse library, it is already loaded.

Question 4
A box contains 3 coins: one of them is a fair coin, with the probability of head and tail both 0.5. The other two coins are both biased in the same way: the probability of head is 0.3, and the probability of tail is 0.7. One of the coins is selected randomly, and tossed 10 times. The random variable X is the number of heads.
Following some of the examples we did in the class, simulate this process, and answer the two questions:
What is the probability that exactly 5 of the tosses will be heads?
Given that exactly 5 of the tosses were heads, what is the probability that the coin was the fair coin?
eval = FALSE

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