Sample Functions: The Mean Value of the Random Variable

The random number generator in a computer generates three-digit numbers that are uniformly distributed between 0.000 and 0.999 at at rate of one random number per second starting at t=0. A sample function from a random process is generated by summing the 10 most recent random numbers and assigning this sum as the value of the sample function during each 1 second time interval. The sample functions are denoted as X(t) for t>=0.

A) Find the mean value of the random variable X(4.5).
B) Find the mean value of the random variable X(9.5).
C) Find the mean value of the random variable X(20.5)

Solution Preview

A) The random variable we have is X(4.5), which means that a sample function from a random process is generated by summing 45(4.5*10 ie,for 1 second the random numbers are 10 then for 4.5 seconds means 4.5*10) most recent random numbers and assigning this sum as the value of the sample function during each 4.5 second time interval.
The mean of ...

Solution Summary

This response calculates the mean value of the random variable within a sample function.

... We could not, for example, get 2.5 heads. ... or graph of the probability density function f(x ... Since continuous probability functions are defined for an infinite ...

... Let X be the number defectives pieces in the sample. ... σ calculated the probabilities The Excel function for normal probability is =normdist(x,mean,sd,0). ...

... to determine whether it is a probability function: P(x ... the quality of a production process, samples of size ... what is Px(â?¤2)? Remember that <= means equal to ...

...means into a column adjacent to the first sample of means of size 15 ... Use MegaStat's Histogram function in the 'Frequency Distribution' procedure again with a ...

... For example, if buses arrive at a given bus ... b), if its probability density function is constant ... The cumulative distribution functions of two independent random...

... The mean value in rent-stabilized units is high with high ... The probability density function is given by P( X = x ... In a sample of 20 individuals taken from a cross ...

... b. Find P(X=1). c. Find P(X=2). d. Find the probability mass function of X. e. Find the mean of X ... Let X be the number of sampled components that are defective. ...

... 15.48) A random sample of 50 observations yielded the following ... For c, we could use function 1-BINOMDIST(2,25 ... 8.35 X is normally distributed with mean 250 and ...

... is also called probability mass function or simply probability function. ... but tends to symmetry when the mean λ becomes ... a situation in which in a sample of n ...