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naspek
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If X has the probability mass function f(x) = k / x! (x=0,1,2,...),
what is the value of k?
what is the value of k?
i don't know.. is it infinity?HallsofIvy said:I think you mean "probability density function".
The total probability must be 1.
[itex]\sum_{x=0}^\infty k/x!= k\sum_{x=0}^\infty 1/x!= 1[/itex]
Do you know what that sum is?
HallsofIvy said:You probably have not taken calculus yet, but if you had you would have learned that
[tex]e^x= \sum_{n=0}&\infty \frac{x^n}{n!}[/tex].
Do you know what an "exponential probability distribution" is?
A probability mass function (pmf) is a mathematical function that describes the probability of a random variable taking on a specific value. It maps each possible value of the random variable to its probability of occurring.
A pmf is used for discrete random variables, while a pdf is used for continuous random variables. A pmf gives the probability of a specific value occurring, while a pdf gives the probability of a range of values occurring.
A pmf must satisfy two properties: 1) The probabilities must be non-negative, and 2) the sum of all probabilities must equal 1. This ensures that all possible outcomes are accounted for and that the probabilities are accurate.
A pmf is used to calculate the probability of a specific outcome or set of outcomes occurring. It can also be used to calculate the mean, variance, and other statistical measures of a random variable.
No, a pmf is only applicable for discrete random variables. For continuous random variables, a probability density function (pdf) must be used.