Probability Distributions and Random Variables Quiz

Continuous random variable

They are represented by probability density functions

They involve integration over the entire range of the random variable

<p>Continuous random variables can take on an infinite number of possible values within a specified range, while discrete random variables can only take on a finite or countably infinite number of distinct values. The probability distribution for continuous random variables is described by probability density functions, while the probability distribution for discrete random variables is described by probability mass functions.</p> Signup and view all the answers

<p>An example of a continuous probability distribution is the normal distribution, described by the probability density function $f(x) = \frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}$. An example of a discrete probability distribution is the binomial distribution, described by the probability mass function $P(X=k) = {n \choose k}p^k(1-p)^{n-k}$.</p> Signup and view all the answers

<p>The expectation of a continuous random variable X with probability density function $f(x)$ is given by $E(X) = \int_{-\infty}^{\infty} xf(x)dx$. The variance of X is given by $Var(X) = E(X^2) - [E(X)]^2 = \int_{-\infty}^{\infty} x^2f(x)dx - [\int_{-\infty}^{\infty} xf(x)dx]^2$.</p> Signup and view all the answers

<p>range</p> Signup and view all the answers

<p>values</p> Signup and view all the answers

<p>Random Variable</p> Signup and view all the answers