A robot is going to attempt the same task 100 times. Each time it tries, it will either succeed or fail to succeed in completing the task. Say the robot does not learn from its tries, so each attempt at the task is independent of the others. On a given attempt, the probability of the robot succeeding is 0.85. Let X be the random variable of the number of times this robot is able to succeed in completing the task. a. What type of distribution can be used for the random variable X? What are it’s parameters? b. What is the expected number of times the robot will succeed? What is the variance? c. What is the probability that the robot succeeds less than or equal to 80 times? Write out the theoretical form and use R to compute the numerical value.
A robot is going to attempt the same task 100 times. Each time it tries, it will either succeed or fail to succeed in completing the task. Say the robot does not learn from its tries, so each attempt at the task is independent of the others. On a given attempt, the probability of the robot succeeding is 0.85. Let X be the random variable of the number of times this robot is able to succeed in completing the task.
a. What type of distribution can be used for the random variable X? What are it’s parameters?
b. What is the expected number of times the robot will succeed? What is the variance?
c. What is the probability that the robot succeeds less than or equal to 80 times? Write out the theoretical form and use R to compute the numerical value.
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