A shopkeeper hires vacuum cleaners to the general public at 5$ per day. The mean daily...

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Statistics

A shopkeeper hires vacuum cleaners to the general public at 5$per day. The mean daily demand is 2.6. Suppose the demand followsPoisson distribution. (a) Calculate the expected daily income fromthis activity assuming an unlimited number of vacuum cleaners isavailable (b) Find the probability that the demand on a particularday is: 0, exactly 1, exactly 2, exactly 3 or more than 3; (c) Ifonly 3 vacuum cleaners are available for hire calculate the mean ofthe daily income. A nearby large store is willing to lend vacuumcleaners at short notice to the shopkeeper, so that she is able tomeet the demand. However, this shop will charge Â£2 per day for thisservice regardless of how many, if any, cleaners are borrowed.Would you advice the shopkeeper to take this offer?

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Solution NOTE The question gives two monetary units A shopkeeper hires vacuum cleaners to the general public at 5 per day this shop will charge 2 per day for this service is taken as the common monetary unit Backup Theory If a random variable X Poisson ie X has Poisson Distribution with mean then probability mass function pmf of X is given by PX x e xx See Answer

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