Assignment Task:
Task:
Question 1 For each question, please write the code you used on R studio. Binomial distribution. We have an experiment with 6 marbles of 2 different colors (2 reds and 4 blacks) where we will try the binomial distribution.
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2. What is the probability to draw exactly 2 red marbles in 6 draws (by putting back the marbles each time)?
3. Compare that result with an experiment where you draw only 2 times. What’s the new probability?
4. Add 3 black marbles. What is the probability to draw 4 red marbles and less if you make 6 draws?
5. Make a graphic of probability density.
6. Make a graphic of the distribution function. Normal distribution. The length of male pikes (a species of fish) is on average 382 mmm with a standard deviation of 37.9 mm.
1. If we consider that the length of captured fishes (males) follow the normal distribution, what is the probability to catch a male with a length superior to 432 mm.
2. If the sample has 200 fishes, how many fishes would be in every class. Choose the classes yourself and explain why you chose them.
3. Present your results in a graphic. Exponential distribution. Earthquakes always occur in the world. Millions of small earthquakes (too small to be noticed) occur every year. Major earthquakes (over 7 on the Richter scale) occur about 1 time every year. With a λ=0.156, calculate:
1. Probability to have an earthquake with more than 7.5 on the Richter scale.
2. Probability to have an earthquake between 3 and 8 on the Richter scale.
3. Arithmetic mean and variance. The number of fires is given on table 2. We want the probability for a fire to occur (Pa) and the probability that a fire isn’t going to occur (Pb).
1. Which distribution are you going to use?
2. Estimate Pa and Pb, show your steps.
3. Make the histogram of theoretical probabilities (according to the chosen distribution) and of relative frequencies. Does the chosen model represent well the observed datas?
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