The joint probability mass function of x and y is given by p(1,1)=0.4 p(2,1)=0.05, p(3,1)=0.1, p(1,2)=0.05, p(2,2)=0, p(3,2)=0.05, p(1,3)=0.1, p(2,3)=0.05, p(3,3)=0.2 (a) compute the conditional mass function of y given x=2: p(y=1|x=2)= 0.5 p(y=2|x=2)= 0 p(y=3|x=2)= 0.5 (b) are x and y independent? i. yesii. no (c) compute the following probabilities: i. p(x+y> 4)= ii. p(xy=3)= iii. p(xy> 2)=

Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?