Consider a Gaussian distributed random variable with zero mean and standard deviation - - The value of its cumulative distribution function at the origin will be

Cumulative distribution function is defined as nbsp; nbsp; nbsp;F(a)=∫_ ∞^af(x)dx So, nbsp; nbsp; nbsp;F(0)=∫_ ∞^0f(x)dx=12 ...

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Engineering Mathematics

Normal Distribution Properties

Consider a Ga...

Question

Consider a Gaussian distributed random variable with zero mean and standard deviation $σ .$ The value of its cumulative distribution function at the origin will be

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0.5

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10 σ

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Solution

The correct option is B 0.5
Cumulative distribution function is defined as

$F (a) = \int_{- \infty}^{a} f (x) d x$

So, $F (0) = \int_{- \infty}^{0} f (x) d x = \frac{1}{2}$

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Consider a Gaussian distributed random variable with zero mean and standard deviation σ. The value of its cumulative distribution function at the origin will be

The correct option is B 0.5Cumulative distribution function is defined as F(a)=∫a−∞f(x)dx So, F(0)=∫0−∞f(x)dx=12

Consider a Gaussian distributed random variable with zero mean and standard deviation $σ .$ The value of its cumulative distribution function at the origin will be

The correct option is B 0.5
Cumulative distribution function is defined as

$F (a) = \int_{- \infty}^{a} f (x) d x$

So, $F (0) = \int_{- \infty}^{0} f (x) d x = \frac{1}{2}$