Question

A random Gaussian process x has a mean of 2.5 and variance of 0.36. Calculate the probability of the random variable having a value less than 3.

Answer 1

Answer: 0.79758

Explanation:

Given that :

Mean (m) = 2.5

Variance = 0.36

Thw standard deviation = sqrt(variance) = sqrt(0.36) = 0.6

The probability of the random variable having a value less than 3 is obtained by:

P(x < 3)

Using the relation to obtain the standardized Zscore :

Z = (x - m) / s

Z = (3 - 2.5) / 0.6

Zscore = 0.8333333

p(Z < 0.833) = 0.79758 ( Z probability calculator)