Answer:
a) k should be equal to 3/16 in order for f to be a density function.
b) The probability that the measurement of a random error is less than 1/2 is 0.7734
c) The probability that the magnitude of a random error is more than 0.8 is 0.164
Step-by-step explanation:
a) In order to find k we need to integrate f between -1 and 1 and equalize the result to 1, so that f is a density function.
16k/3 = 1
k = 3/16
b) For this probability we have to integrate f between -1 and 0.5 (since f takes the value 0 for lower values than -1)
c) For |x| to be greater than 0.8, either x>0.8 or x < -0.8. We should integrate f between 0.8 and 1, because we want values greater than 0.8, and f is 0 after 1; and between -1 and 0.8.