Скачать или смотреть The geometric distribution.The geometric random variable . The pmf of a geometric random variable.

What is probability density function? What is a probabiliy mass density? the geometric random.distribution. the mean and the pmf oa geometric random variable.
part 1
Today, we're going to talk about the geometric distribution. Hey geometric distribution is a distribution of discrete random variable. It's the geometric distribution. That occurs in experiments were repeated, trials possess the following properties. There are any repeated trials. Each trial has two possible outcomes In general. Now, when as success and failure, Trials are repeated until a predetermined. The number of success Is reached All, trials are identical and independent thus the probability for Success Remains the Same for each trial. We introduced the geometric. Random variable X X is the number of trials required to obtain. The first success It's gonna be zero one, two, three, and Etc.
part 2
The mean of geometric random variable is given by 1 over P where pi is the probability. We can also Define the variance of the geometric random variable as 1 minus P. Over P Square. We can have some examples Where an electrician inspecting cable one yard at a time. For defect counts. We can also see the number of times where we here to go. After 106 failures, We can also see the number out of time that one can go to hospital after having missing the hospital for 36 times. In this example, we're going to use a series Taylor series to compute the geometric distribution. Mean, We need to pay attention to these computation here because it's going to be useful later. We're going to prove that the geometric distribution is a probability Mass function. We will have to prove that by using many techniques. And one of the techniques is that some of the series
part 3
We're also going to prove that function is a

probability density function. First, we need to show that F is positive and also that the integral between minus infinity and infinity of the function is one. The key idea here is is that we can use integration. We can use any integration techniques that we have learned so far to prove our result, for the discrete case, we just use the sum and series are b. R will are Will be very useful in Computing. The mean, in our case here,
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