Suppose a company purchases 5 computers from a recent shipment of computers to a retail store. The shipment contained 20 computers in which 4 are defective. Let X be a random variable representing the number of defective computers the company obtains. 1. What is the pmf of X? 2. What is the probability that the company will receive 2 or more defective computers? 3. Compute P(1 less than or equal to X < 3). What is the expected value of X?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Suppose a company purchases 5 computers from a recent shipment of computers to a retail store. The shipment contained 20 computers in which 4 are defective. Let X be a random variable representing the number of defective computers the company obtains.
1. What is the pmf of X?
2. What is the probability that the company will receive 2 or more defective computers?
3. Compute P(1 less than or equal to X < 3). What is the expected value of X?
Suppose a company purchases 5 computers from a recent shipment of computers to a retail store. The shipment contained 20 computers in which 4 are defective. Let X be a random variable representing the number of defective computers the company obtains.
Condition for binomial distribution:
- Each trail has only two outcomes.
- Number of trails should be fixed.
- Probability of each trail should be same.
- The trails should be independent.
Here, each trails has only two outcomes either defective or non-defective, number of trails is fixed which is 5. Probability of each trail is same and trials are independent. Therefore, all the above conditions are satisfied.
Step by step
Solved in 4 steps with 3 images