Asked Dec 1, 2019

what are the mean, variance, pdf, and cdf of the following distributions

  •  Normal
  • Exponential
  • Uniform
  • t-distribution w v degrees of freedom
  • chi-squared distribution with v degrees of freedom
  • F-distribution wit v1 and v2 degrees of freedom
  • bernoulli
  • binomial
  • poisson

Expert Answer

Step 1

The mean, variance, pdf and CDF of the following distributions are as given below:

Step 2


Normal distribution:

Let x be a random variable that follows normal distribution then its PDF, CDF, mean and variance are as given below:


Image Transcriptionclose

Mean E(x)= Variacne V(x)o Pdf ((x-u) 1 f(x)2 0,0therwise cdf (1-u7 1 dx F(x)= /2 πσ

Step 3


Exponential distribution:

Let x be a random variable that follows exponential distribution then...


Image Transcriptionclose

Mean: 1 E(x) Variacne 1 (x)4 pdf re x 20 f(x, A)= [0,x<0 cdf (1-e,x20 (0,x<0 F(x)


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