Show that a function given by its graph is a probability density function.function distribution

Given a function as how can we prove that? It is a probability density function. What is a probability density function? What's a distribution? What's the function distribution? What's the cumulative distribution function? What's an exponential function? What's a uniform distribution? What's an inexponential distribution. And what's a random variable that comes with Probability? You don't see the function. What's also the probability must function? How can we find the mean, the median and the mode from the graph, Given the graph of the function? How can we say that? It is a probability density function. These problems we're going to solve here in these videos. So we're going to start with the normal distribution. And after that, we're going to use the uniform disturbution and the exponential distribution Later, we're going to model all of these using some Compose random valuable To be able to solve all of this. We first need to show that office positive That the integral of F between minus infinity and infinity is one. These are two conditions to show that I have is a probability density function. To find the mean, we need to integrate Times X between minus infinity. And plus infinity Later. We're gonna find the variance and the standard deviation for these random variables. We will compute all of these using the, the notion of improper integrals. This notion must be understood to be able to compute all of these values. Later, we gonna Define applications and see that we can have applications in engineering In thermodynamics in computer science. And in real life,
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