maria_01 said:Homework Statement
The random variable x takes on the values 1, 2, or 3 with probabilities (1 + 3k)/3, (1 + 2k)/3, and (0.5 + 5k)/3, respectively.
Homework Equations
i. Find the appropriate value of k.
ii. Find the mean.
iii. Find the cumulative distribution function.
The Attempt at a Solution
maria_01 said:Also if I knew how to do it, I wouldn't be asking for help. My attention is not to just get the answers but atleast know which formulas to use and how to imply them. I"m really stuck at cumulative distribution function.
maria_01 said:I'm an IT person clueless of statistics.
A cumulative distribution function (CDF) is a mathematical function that represents the probability of a random variable taking on a certain value or falling within a certain range. It is used to determine the likelihood of an event occurring based on the probability distribution of the random variable.
A probability distribution function (PDF) gives the probability of a specific outcome or value of a random variable occurring. A cumulative distribution function, on the other hand, gives the probability of a random variable falling below a certain value.
The cumulative distribution function is useful in analyzing and understanding probability distributions. It allows us to determine the probability of a random variable falling within a certain range, which is important in making predictions and decisions based on data.
To find the cumulative distribution function, you must first determine the probability distribution function of the random variable. Then, you can use integration or summation to find the cumulative probabilities for each possible outcome or range of values.
The cumulative distribution function has many practical applications in fields such as statistics, finance, and engineering. It can be used to model and analyze real-world phenomena, make predictions, and evaluate risk. In finance, it is commonly used to calculate the probability of a stock price falling below a certain level. In engineering, it can be used to determine the likelihood of a product failing under certain conditions.