Random Variable
A random variable is one whose values are determined by the results of a randomly occurring phenomenon. In other words, its value is not constant, but it may assume any potential values of that occurrence (experiment) (Lambert, 2018). Y is a discrete random variable if its values or representative area can be counted. On the contrary, it is considered a continuous random variable if it’s quantities or representative array of values are not quantifiable and it accepts any numbers on the reference axis or its interval.
Explanation
Y is a discrete random variable if its values or sample space can be counted. For instance, the number of people who arrived at the office between 7:00 A.M and 8:00 AM on a Monday. Conversely, Y is considered a continuous random variable if the quantities or representative array of values are not quantifiable. For example, the lifespan of a car battery. Here, Y may have any value between 0 and ∞, making it a continuous random variable.
Binominal Experiment
A binomial experiment has four properties and may be utilized in a binomial distribution if the four conditions listed below are met:
- The representative sample (n) is constant;
n = 15 in this case; hence this hypothesis is true.
- There are only two possibilities that may occur when a function is replicated: success or failure;
In this case, the laptop can either match the standards or fall short; this premise is true.
- The likelihood of success is the same and fixed for each duplication;
In this case, the percentage of laptops manufactured that meet standards are set at 0.95; therefore, this hypothesis is fulfilled.
- The simulations (or trials) are self-contained.
Given all assumptions are met, a binomial distribution may be employed to depict this operation.
- If more than one laptop does not match the criteria, the whole batch must be examined, which is unnecessary. The needed probability is P(X > 1), which may be calculated using the excel function “1-BINOMDIST(1,15,0.05, TRUE)”. The probability obtained is 0.170953.
- Accepting the lot would be wrong if the number of defects is less than or equal to 1, provided the faulty rate is 0.25. The needed probability is P(X = 1), which may be calculated using the function “BINOMDIST(1,15,0.25, TRUE)” in Excel. The probability obtained is 0.08018.
References
Lambert, B. (2018). A student’s guide to Bayesian statistics. Sage.