Most computer languages include a function that can be used to generate random numbers. In Excel, the RAND function can be used to generate random numbers between 0 and 1. If we let x denote a random number generated using RAND, then x is a continuous random variable with the following probability density function.

 
a. Graph the probability density function.

b. What is the probability of generating a random number between .25 and .75?

c. What is the probability of generating a random number with a value less than or equal to .30?

d. What is the probability of generating a random number with a value greater than .60?

e. Generate 50 random numbers by entering = RAND() into 50 cells of an Excel worksheet.

f. Compute the mean and standard deviation for the random numbers in part (e).

for 0 sxs1 f(x)= %3! elsewhere