Finding Alpha in a Continuous Probability Distribution

In summary, the conversation discusses the difficulty of using Latex and a question about finding the value of alpha in a continuous random variable with a given cumulative distribution. The conversation also mentions the importance of the probability distribution being equal to 1 and the need to possibly convert to a probability density function before continuing to work on the problem. The answer is determined to be 1/3 based on the function being continuous and having a probability of 1 at infinity.
  • #1
denian
641
0
i really don't know how to ue the Latex. it doesn't work although i try it for many times.

so, I am new to this chapter. maybe this question is easy to be solved, but i can't get it.

a continuous random variable X has cumulative distribution as attached.
the question is what is the value of alpha.
i try doing like this but it doesn't give any answer though.

F(-1) = 0 = (alpha)(-1)+(alpha)

what is the working so that i can get the answer.
 

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  • #2
Originally posted by denian
it doesn't work although i try it for many times.

blasphemy!

ok, if f(x) is a probability distribution I guess what matters the most is that:
[tex]\int_D f(x)dx = 1[/tex]
where D is the interval where f is defined (you didn't mentioned it in your question...)
 
  • #3
but that is a cumulative distribution.
i copy the whole thing from the question.

do i need to change it to probability density function first, then continue to work on it.
 
  • #4
oh...
then alpha is 1/3 because as I remember [itex]f(\infty) = 1[/itex]
and also the function is continuous...
 
  • #5
ok. thank you
 
Last edited:

1. What is a continuous probability distribution?

A continuous probability distribution is a mathematical function that describes the probabilities of all possible outcomes of a continuous random variable. It represents the relative likelihood of observing different values of the variable within a given range.

2. How is a continuous probability distribution different from a discrete probability distribution?

A continuous probability distribution represents outcomes that can take on any value within a given range, while a discrete probability distribution represents outcomes that can only take on specific values. This means that a continuous probability distribution has an infinite number of possible outcomes, while a discrete probability distribution has a finite number of possible outcomes.

3. What is the standard notation used for a continuous probability distribution?

The standard notation used for a continuous probability distribution is f(x), where x represents the random variable and f(x) represents the probability density function (PDF). The area under the curve of the PDF represents the probability of obtaining a specific value or range of values of the random variable.

4. What are some common examples of continuous probability distributions?

Some common examples of continuous probability distributions include the normal distribution, the exponential distribution, and the uniform distribution. The normal distribution is commonly used to model natural phenomena, such as heights or weights of a population. The exponential distribution is often used to model the time until an event occurs, such as the time until a light bulb burns out. The uniform distribution is used when all outcomes in a given range are equally likely.

5. How is the mean and variance of a continuous probability distribution calculated?

The mean (μ) and variance (σ^2) of a continuous probability distribution can be calculated using the following formulas:

Mean (μ) = ∫xf(x) dx (the integral of x multiplied by the probability density function)

Variance (σ^2) = ∫(x-μ)^2f(x) dx (the integral of (x-mean)^2 multiplied by the probability density function)

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