Let X denote th roportion of allotted time that a randomly selected student spends working on a particular aptitude test, and suppose the probability density fuction, p(x) of X is: {f(x)= (theta + 1)x^theta when x is greater than or equal to zero and less than or equal to 1} and {f(x)= 0 otherwise where -1 < theta.
a. find and graph the cumlative distribution function, F(x)= P(X is less than or equal to x)of X.
B. Find the probability that a randomly selected student spends at least three quarters of the allotted time on the test.
c.Find the probability that a randomly selected student spends between eighty and ninety percent of the time on the test.
d. Find the expected value of X. E(X)
E. Find the reliability function, R(t)=P(X > t)
f. Find the failure rate of X.