Question

Given: P(X = 0) = 0.81, P(X = 1) = 0.02, P(X = 2) = 0.16, P(X = 3) = 0.01. Please solve Question 11, 12, and 13. You don't have to solve 7-10 since I already solved it correctly and provided you those values.

Prompt 3: A certain system can experience three different types of defects. Let
Ai ,i=1,2,3 be the event that the system has a defect of type i. Suppose that (P(A_1) = 0.17, P(A_2) =

Answer 1

Questions 11 and 12 are related to probability distributions, where the probabilities must sum to 1, and the expected value is calculated by summing the products of variable values and their probabilities.

Step-by-step explanation:

This student is dealing with concepts from probability and specifically, problems related to probability distributions. For question 11, the probability values given for different outcomes of the random variable X, which denotes some aspect of the system with potential defects, should sum to 1. If they added up to 1.10, there would be an error since the total probability must be 1. In question 12, the student is asked to find the expected value (or mean) of variable X based on the given probabilities; the formula for this is the sum of each value of X multiplied by its corresponding probability. For question 13, we lack context to answer, as the continuation of the question or additional information is not provided; thus, it’s imperative to ask for more details to calculate any further statistics like variance or standard deviation.