Exercise 2. Let X be a discrete random variable with the cumulative
distribution function
0 x<1 
F(x)= 0.5 1≤x<3 1 x≥3
(1) Calculate the probability P {X ≤ 3}
(2) Calculate the probability P {1 ≤ X ≤ 2}

An electrical motor raises a 50kg load at a construct velencity .calculate the power of the motor, if it takes 40sec to raise the load through a height of 24m(take g =9.8n/g)

Adouble-strand no. 60 roller chain is used to transmit power between a 13-tooth driving sprocket rotating at 300 rev/min and a 52-tooth driven sprocket. a) what is the allowable horsepower of this drive? b) estimate the center-to-center distance if the chain length is 82 pitches. c) estimate the torque and bending force on the driving shaft by the chain if the actual horsepower transmitted is 30 percent less than the corrected (allowable) power.

At 12 noon, the count in a bacteria culture was 400; at 4: 00 pm the count was 1200 let p(t) denote the bacteria cou population growth law. find: (a) an expression for the bacteria count at any time t (b) the bacteria count at 10 am. (c) the time required for the bacteria count to reach 1800.