A box contains 25 marbles, where each marble has elther green or brown color. It is...

 

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A box contains 25 marbles, where each marble has elther green or brown color. It is given that there are 18 green marbles in this box. a. The number X of chosen marbles until we choose 3 brown marbles from this box with replacement has a ? v distribution, where its expectation is E(X) b The number Y of chosen brown marbles when we choose 6 marbies from this box without replacement has a ? v distribution, where its expectation is E(Y) e The number Z of chosen brown marbles when we choose 6 marbles trom this box with replacement has a distribution. where its expectation is E(Z) - Note: You can eam partial credit on thia problem Problem 2. (4 points) it is glven that the number K of pulses arrive at the counter per minute has a Poisson distribution, where pulses arrive at the counter at an average rate of 6.5 per minute a Find the expected number E (K) of pulses per minute. E(K) - b Find the varlance Var (K) of K Var (K) - c Find the standard deviation e of K d. Compute the following probability P(-2< Xs 1) = A box contains 25 marbles, where each marble has elther green or brown color. It is given that there are 18 green marbles in this box. a. The number X of chosen marbles until we choose 3 brown marbles from this box with replacement has a ? v distribution, where its expectation is E(X) b The number Y of chosen brown marbles when we choose 6 marbies from this box without replacement has a ? v distribution, where its expectation is E(Y) e The number Z of chosen brown marbles when we choose 6 marbles trom this box with replacement has a distribution. where its expectation is E(Z) - Note: You can eam partial credit on thia problem Problem 2. (4 points) it is glven that the number K of pulses arrive at the counter per minute has a Poisson distribution, where pulses arrive at the counter at an average rate of 6.5 per minute a Find the expected number E (K) of pulses per minute. E(K) - b Find the varlance Var (K) of K Var (K) - c Find the standard deviation e of K d. Compute the following probability P(-2< Xs 1) =