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Probability Function ▼Math Symbols ▲Math Symbols

Common forms and functions
  • x+y x+y
  • x·yx*y
  • x/yx÷y
  • xyx**y
  • √xsqrt(x)
  • x!factorial(x)
  • ln(x)log(x)
  • exexp(x)
  • log10(x)log(x, 10)
  • log2(x)log(x, 2)
  • sin(x)sin(x)
  • cos(x)cos(x)
  • tan(x)tan(x)
  • cot(x)1/tan(x)
  • atan(x)atan(x)
  • asin(x)asin(x)
  • acos(x)acos(x)
  • sinh(x)sinh(x)
  • cosh(x)cosh(x)
  • tanh(x)tanh(x)
  • eE
  • πpi
A Poisson process is a situation in which a phenomenon occurs at a constant average rate. Each occurrence is independent of all other occurrences; in a Poisson process, an event does not become more likely to occur just because it’s been a long time since its last occurrence. The location of potholes on a highway or the emission over time of particles from a radioactive substance may be Poisson processes.

The probability density function:

f(x) = 


describes the relative likelihood of an occurrence at time or position x, where ? describes the average rate of occurrence.
The probability P (a < x < b) of an event occurring in the interval between a and b is given by:

\int_{a}^{b} f(x) \text{d}x

  •  Calculate the probability for the case in which a and b are both positive (assume a < b)

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Probability Function ▼Math Symbols ▲Math Symbols

Common forms and functions
  • x+y x+y
  • x·yx*y
  • x/yx÷y
  • xyx**y
  • √xsqrt(x)
  • x!factorial(x)
  • ln(x)log(x)
  • exexp(x)
  • log10(x)log(x, 10)
  • log2(x)log(x, 2)
  • sin(x)sin(x)
  • cos(x)cos(x)
  • tan(x)tan(x)
  • cot(x)1/tan(x)
  • atan(x)atan(x)
  • asin(x)asin(x)
  • acos(x)acos(x)
  • sinh(x)sinh(x)
  • cosh(x)cosh(x)
  • tanh(x)tanh(x)
  • eE
  • πpi
A Poisson process is a situation in which a phenomenon occurs at a constant average rate. Each occurrence is independent of all other occurrences; in a Poisson process, an event does not become more likely to occur just because it’s been a long time since its last occurrence. The location of potholes on a highway or the emission over time of particles from a radioactive substance may be Poisson processes.

The probability density function:

f(x) = 


describes the relative likelihood of an occurrence at time or position x, where ? describes the average rate of occurrence.
The probability P (a < x < b) of an event occurring in the interval between a and b is given by:

\int_{a}^{b} f(x) \text{d}x

  •  Calculate the probability for the case in which a ? 0 and b > 0

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Area of a Smile

  • The region between the curves y=\frac{1}{2} x^{2}-\frac{1}{2} and y=x^{4}-1 is smile shaped. Find the area of that region

    The exact value of the area is :

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