Examples for

Random Variables

A random variable is a statistical function that maps the outcomes of a random experiment to numerical values. Specify the probability distribution underlying a random variable and use Wolfram|Alpha's calculational might to compute the likelihood of a random variable falling within a specified range of values or compute a random variable's expected value.
Expected Value

Compute the expected value of a random variable from a specified probability distribution.

Compute the expected value of a random variable:

expected value of |x|^3, x standard normal
X~Poisson(7.3), EV[3X^4-7]
E[x^2] where x is exponentially distributed
expectation of y^2+2y-1 for y having a gamma distribution
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Probability Computations

Compute the probability that the outcome of a random variable from a specified probability distribution will lie within a range of values.

Compute the probability of an event:

P[-1.2<X<2.3] for X~student t with 12 dof
prob x>5 for x binomial with n=14 and p=.36
x chisquare with 9 dof, prob 3x-5<7
prob X<16 for X~geometric with p=0.1

Compute a conditional probability:

probability that x^2>2 given that x>1, x~standard normal
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