In a particularly addictive game (Helicopter Game) you have to get a helicopter to fly some...

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In a particularly addictive game (Helicopter Game) you have to get a helicopter to fly some distance in arbitrary units. Suppose the distance you travel can be modeled as a random variable D having pdf f(d)= 1.2 (1+0.4d)4 d>0 else Where d is measured in thousands (1 = 1000 units) 1. Determine the 90th percentile distance traveled (i.e. find & such that P(D≤ k) = 0.9). 2. Determine the expected distance traveled on a single run. 3. Determine the variance and standard deviation of the distance traveled. 4. If you have traveled 1500 units so far what is the probability you will travel more than 2000 units total? 5. How many rounds can you expect to play in order to have a round where you travel more than 5000 units? 6. What assumptions must you make in (5)? In a particularly addictive game (Helicopter Game) you have to get a helicopter to fly some distance in arbitrary units. Suppose the distance you travel can be modeled as a random variable D having pdf f(d)= 1.2 (1+0.4d)4 d>0 else Where d is measured in thousands (1 = 1000 units) 1. Determine the 90th percentile distance traveled (i.e. find & such that P(D≤ k) = 0.9). 2. Determine the expected distance traveled on a single run. 3. Determine the variance and standard deviation of the distance traveled. 4. If you have traveled 1500 units so far what is the probability you will travel more than 2000 units total? 5. How many rounds can you expect to play in order to have a round where you travel more than 5000 units? 6. What assumptions must you make in (5)?