human
What is a the Python code you requested given the following:
I am working on the file "Notebooks/quantopian_research_public/notebooks/lectures/Random_Variables/notebook.ipynb".
The first task is:
Changing the value of $p$ from $0.50$ to $0.25$ clearly makes our distribution asymmetric. We can extend this idea of stock price moving with a binomial random variable into a framework that we call the Binomial Model of Stock Price Movement. This is used as one of the foundations for option pricing. In the Binomial Model, it is assumed that for any given time period a stock price can move up or down by a value determined by the up or down probabilities. This turns the stock price into the function of a binomial random variable, the magnitude of upward or downward movement, and the initial stock price. We can vary these parameters in order to approximate different stock price distributions.
Continuous Random Variables
Continuous random variables differ from discrete random variables in that continuous ones can take infinitely many outcomes. They cannot be counted or described as a list. As such, it means very little when we assign individual probabilities to outcomes. Because there are infinitely many outcomes, the probability of hitting any individual outcome has a probability of 0.
We can resolve this issue by instead taking probabilities across ranges of outcomes. This is managed by using calculus, though in order to use our sampling techniques here we do not actually have to use any. With a continuous random variable $P(X = 0)$ is meaningless. Instead we would look for something more like $P(-1 < X < 1)$. For continous random variables, rather than using a PMF, we define a probability density function (PDF), $f_X(x)$, such that we can say:
$$P(a < X < b) = \int_a^b f_X(x)dx$$
Similar to our requirement for discrete distributions that all probabilities add to $1$, here we require that:

$f_X(x) \geq 0$ for all values of $X$
$P(-\infty < X < \infty) = \int_{-\infty}^{\infty} f_X(x) dx = 1$

It is worth noting that because the probability at an individual point with a continuous distribution is $0$, the probabilities at the endpoints of a range are $0$. Hence, $P(a \leq X \leq b) = P(a < X \leq b) = P(a \leq...
Can you write Python code for it?
assistant
#Here is the Python code you requested.

class ContinuousRandomVariable:
    def __init__(self, a = 0, b = 1):
        self.variableType = ""
        self.low = a
        self.high = b
        return
    def draw(self, numberOfSamples):
        samples = np.random.uniform(self.low, self.high, numberOfSamples)
        return samples