Answer Happy

1) The joint probability mass function of X & Y are given below: X 2 3 4 1 0.09 0.03 0.01 0.01 2 0.02 0.15 0.03 0.01 뭉 Y 3 0.01 0.01 0.24 0.04 4 0.00 0.01 0.02 0.32 1) Show that this is a valid joint probability mass function 2) E(XY=2) = ? 3) Corr(X,Y)= ?. Write down the comment 2) An archer hits a bull's-eye with a probability of 0.09, and the results of different attempts can be taken to be independent of each other. If the archer shoots nine arrows, calculate the probability that: 1) Exactly two arrows score bull's-eyes. 2) At least two arrows score bull's-eyes. What is the expected number of bull's-eyes scored? 3) On average there are four traffic accidents in a city during one hour of rush- hour traffic. Use the Poisson distribution to calculate the probability that in one such hour there are (a) no accidents (b) at least six accidents 4) Suppose an archer hits a bull's-eye with a probability of 0.09, and the results of different attempts can be taken to be independent of each other. (a) If the archer shoots a series of arrows, what is the probability that the first bull's-eye is scored with the fourth arrow? (b) What is the probability that the third bull's-eye is scored with the tenth arrow? (c) What is the expected number of arrows shot before the first bull's-eye is scored? (d) What is the expected number of arrows shot before the third bull's-eye is scored?