Statistikk og Simulering

Økt 12. Kontinuerlege stokastise variablar

Mean and variance for a continuous random variable

13.2. Mean and variance for a continuous random variable

The sample mean and variance for a continuous random variable are calculated in the exact same way as we have done for a discrete random variable see formulas given at exercises 32 and 41.

However, in order to calculate the expected value, variance and standard deviation of the population of all possible outcomes we now need to integrate instead of sum over all possible outcomes:

μX = E(X) =xf(x)dx, (28)  σX2 = E((X μ X)2) =(x μ X)2f(x)dx. (29) 

Oppgåve 13.19 Take your sample of 10 uniformly distributed continuous random variables from exercise 52. Compute the sample mean, standard deviation and variance.

Oppgåve 13.20 Calculate the expected value, variance and standard deviation for a uniformly distributed continuous random variable in the interval <0, 1>. Compare your results to the previous exercise.

Oppgåve 13.21 Take your sample of 15 random numbers from exercise 62 generated as the sum of two uniform random variables. Compute the sample mean, standard deviation and variance.

Oppgåve 13.22 Calculate the expected value, variance and standard deviation for the sum of two independent uniformly distributed continuous random variables in the interval <0, 1>. Compare your results to the previous exercise.

Les 7 §5.1 Expected value

§5.2 Dispersion, variance, standard deviation

Oppgåve 13.23 Frisvold og Moe: E5.7, E5.12