the total number of hours measured in units of 100 hours that a family runs a vaccum cleaner over a period of one year is a continuous random variable, x, that has probability density function:
f(X) =
x, 0≤ x ≤1
k-x, 1x2
0 elsewhere
(a) determine that value of k
(b) find the probability that over a period of one year, a family runs their vaccum cleaner less than 110 hours.
also find probability: P [ 0.5≤x ≤ 1.5

Question

the total number of hours measured in units of 100 hours that a family runs a vaccum cleaner over a period of one year is a continuous random variable, x, that has probability density function:
f(X) =
x, 0≤ x ≤1
k-x, 1>x>2
0 elsewhere
(a) determine that value of k
(b) find the probability that over a period of one year, a family runs their vaccum cleaner less than 110 hours.
also find probability: P [ 0.5≤x ≤ 1.5

anonymous · Answer

please help me in solving this problem